AML patients in first complete remission (CR) (CR1) or first complete remission with incomplete blood count recovery (CRi) after induction and consolidation chemotherapy; except young (< 60 years) AML patients in European LeukemiaNet favorable group; (the current trial will exclude young favorable group AML patients), patients could receive any cycle consolidation or no consolidation per the discretion by the treating physician

Must have achieved an objective response (CR/PR) or stable disease (SD) upon completion of scheduled treatment

Patients must have achieved a CR or CRi

Patients who have achieved a CR or CRi must have maintained peripheral blood evidence of a CR or CRi

Patients must have maintained peripheral blood evidence of a remission and must have a CR or CRi, confirmed on restaging bone marrow (BM) aspirate and biopsy

CRITERIA FOR MAINTENANCE THERAPY-STEP 4: Patients must have maintained peripheral blood evidence of a remission and must have a CR or CRi, confirmed on restaging BM aspirate and biopsy

Patient may be receiving or have completed induction therapy within 60 days prior to preregistration to step 0; no more than 300 days may have passed between the first day of induction therapy and preregistration to step 0\r\n* For patients who have completed induction therapy, restaging evaluation must show status of partial (PR) or complete response (CR); post-induction patients with evidence of clinical disease progression are not eligible for preregistration\r\n* Up to two regimens of chemotherapy are allowed as long as a continuous response was ongoing throughout therapy; overall, a partial response needs to have been achieved (using studies at the time of diagnosis as the baseline)\r\n**NOTE: For example, a patient who started treatment with rituximab/bendamustine and was then switched to rituximab(R)-cyclophosphamide, doxorubicin hydrochloride, vincristine sulfate, and prednisone (CHOP) (due to insufficient response or excessive toxicity) would be counted as having received 2 regimens; however, R-CHOP alternating with R-dexamethasone, high-dose cytarabine, and cisplatin (DHAP) as a planned induction regimen would count as one regimen

Patients must have achieved a radiologic complete or partial remission as defined by the Lugano criteria

Completion of remission induction therapy

COHORT 1 PH-NEGATIVE PATIENTS ONLY: Patients must have achieved CR or CRi within 2 cycles of induction/re-induction with blinatumomab\r\n* NOTE: day 1 of post-remission = day 43 of the preceding cycle (+/- 3 days)

COHORT 2 PH-POSITIVE AND PH-LIKE DSMKF PATIENTS ONLY: Newly diagnosed Ph+, newly-diagnosed Ph-like DSMKF, and relapsed/refractory Ph+ patients without prior dasatinib or other 2nd or 3rd generation TKI therapy, must have achieved CR or CRi within 1 cycle of induction with dasatinib/prednisone, or within 2 cycles of re-induction with blinatumomab; relapsed/refractory Ph+ or Ph-like DSMKF patients with prior dasatinib or other 2nd or 3rd generation TKI therapy must have achieved CR or CRi within 2 cycles of re-induction therapy with blinatumomab\r\n* NOTE: day 1 of post-remission = day 85 of the preceding induction cycle (+/- 3 days), or day 43 of the preceding re-induction cycle (+/- 3 days) as applicable

Patients must be registered to Step 2 within 28 days after count recovery; (Note: there is no maximum allotted time period for count recovery, providing patient remains in CR or CRi)

Prior or concurrent malignant disease unless in complete remission for more than five years

Patients must have achieved a response to induction chemotherapy (either CR or PR by Cheson 2007 criteria) and be without known progression

leukemia in 1st relapse with initial CR duration < 6 months,

Mantle cell NHL: may be treated in first complete remission (CR); (diagnostic lumbar puncture [LP] required pre-transplant)

Calculated Cr Cl >= 30 ml/min; eligible for reduced dose methotrexate

failed to achieve a complete response after 6 or more cycles; and/or

The subjects should be in first or second CR (including CR and SCR) or PR (including PR and VGPR)

Biopsy-proven intermediate or high-grade non-Hodgkin’s lymphoma, meeting one of the following criteria (timeline 8 months prior to enrollment):\r\n* In partial remission\r\n* Relapsed after initial complete remission\r\n* Failed induction therapy, but responds to salvage therapy (i.e., chemosensitive disease)\r\n* In complete remission with high-risk features as specified by the International Prognostic Index

Biopsy-proven Hodgkin’s lymphoma, meeting one of the following criteria (timeline 8 months prior to enrollment)\r\n* In first, or greater relapse after initial complete remission\r\n* In partial remission\r\n* Failed induction therapy, but responds to salvage therapy (i.e., chemosensitive disease)

Biopsy-proven Burkitt’s lymphoma, meeting one of the following criteria (timeline 8 months prior to enrollment):\r\n* In second complete remission after relapse following initial complete remission\r\n* Failed induction therapy, but responds (very good partial remission, complete remission, or near complete remission) to salvage therapy (i.e., chemosensitive disease)

NOTE: Patients meeting the following criteria are exempt from the 8 month timeline and do not require additional biopsy:\r\n* Patients who have never achieved a complete remission on the last biopsy-proven site of disease and went on to the next therapy then achieved a complete remission\r\n* Patients who relapsed quickly (within 3 months of their last chemotherapy) and now have achieved a complete remission with salvage therapy

Achieved at least a partial response (PR) to therapy

Patients must be considered bevacizumab-resistant, i.e.; have a treatment-free interval following a response to bevacizumab (complete response [CR], partial response [PR], or stable disease [SD]) of less than 6 months, or have progressed during treatment with a bevacizumab-containing therapy

Complete first remission (CR1) at high risk for relapse

Complete second remission (CR2).

Complete first remission (CR1) at high risk for relapse

Complete second remission (CR2).

In view of the principal investigator (PI) and the primary oncologist, there must be no available alternative curative therapies or subject has declined to pursue alternative therapy; and subjects must be either ineligible for allogeneic stem cell transplant (SCT), have refused SCT, recurred after SCT, or have disease activity that prohibits SCT at the time of enrollment\r\n* Chemotherapy refractory disease in subjects with B-ALL is defined as progression or stable disease after two lines of therapies\r\n* Recurrence of disease after achieving a complete response (CR)\r\n* Subjects with persistent or relapsed minimal residual disease (MRD) (by flow cytometry, polymerase chain reaction [PCR], fluorescence in situ hybridization [FISH], or next generation sequencing) require verification of MRD positivity on two occasions at least 4 weeks apart\r\n* Subjects with Philadelphia chromosome positive acute lymphoblastic leukemia (Ph+ALL) subjects are eligible if they progressed, had stable disease or relapsed after two lines of therapy, including tyrosine kinase inhibitors (TKIs)\r\n* Subjects with recurrence of isolated central nervous system (CNS) relapse after achieving complete remission (CR); if relapsed with MRD, will require verification of MRD positivity on two occasions at least 4 weeks apart

Acute lymphoblastic leukemia (B- or T-acute lymphoblastic leukemia [ALL])\r\n* Complete response (CR)1-ultra high risk features\r\n** Unfavorable cytogenetics\r\n** Hypodiploidy\r\n** Induction failure\r\n** Minimal residual disease (MRD) positive after consolidation\r\n* CR2\r\n** Any of the high risk features listed in CR1\r\n** B-ALL: any relapse considered eligible for transplant \r\n** T-ALL\r\n* CR 3-any

Acute myeloid leukemia\r\n* MRD > 5% at day 22 induction 1\r\n* MRD > 0.1% after induction 2\r\n* FMS-like tyrosine kinase (FLT)/internal tandem duplication (ITD) with allelic ratio > 0.4 and MRD > 0.1% at day 29 induction 1\r\n* Translocation (6:9), (8:6), (16:21), monosomy7, monosomy 5, 5q.\r\n* M7 without translocation (1;22)\r\n* M7 with KMT2A rearrangements, inv(16)(p13.3q24.3) [CBFA2T3-GLIS2] or t(11;12)(p15;p13) [NUP98-KDM5A]\r\n* AML in 2nd or subsequent CR\r\n* Therapy related or secondary AML\r\n* Refractory anemia with excess blasts (RAEB) 2

Acute Lymphoblastic Leukemia (ALL) in first complete remission (CR1) that is NOT considered favorable-risk as defined by the presence of at least one of the following: Adverse cytogenetics such as t(9;22), t(1;19), t(4;11), other Mixed Lineage Leukemia (MLL) rearrangements; White blood cell counts of greater than 30,000/mcL (B-ALL) or greater than 100,000/mcL (T-ALL)at diagnosis; Recipient age older than 30 years at diagnosis; Time to CR greater than 4 weeks

Acute Leukemias in 2nd or subsequent CR

Biphenotypic/Undifferentiated/Prolymphocytic Leukemias in first or subsequent CR, adult T-cell leukemia/lymphoma in first or subsequent CR

Burkitt's lymphoma: second or subsequent CR

Participant has confirmed, morphologically documented AML in CR1. For the purposes of registration, CR1 will be defined as < 5% blasts in the BM with no morphologic characteristics of acute leukemia (e.g., Auer Rods) in the BM with no evidence of extramedullary disease such as central nervous system involvement or granulocytic sarcoma.

Participant has not received more than 2 cycles of induction chemotherapy to achieve CR1. The induction cycles can be the same regimen or different regimens. The regimen(s) may contain conventional agents, investigational agents, or a combination of both.

Participants with CR with incomplete count recovery (CRp or CRi) are allowed. Incomplete platelet recovery (CRp) is defined as CR with platelet count < 100 x 109/L. Incomplete blood count recovery (CRi) is defined as CR with residual neutropenia < 1 x 109/L with or without complete platelet recovery. Red blood cell count (RBC) and platelet transfusion independence is not required.

The maximum time allowed from establishment of CR1 to registration is 12 months.

Participant has confirmed ongoing morphologically documented AML in CR1. For the purposes of randomization, CR1 will be defined as < 5% blasts with no morphologic characteristics of acute leukemia (e.g., Auer Rods) in the BM with no evidence of extramedullary disease such as central nervous system involvement or granulocytic sarcoma.

Patients must have received pre-study nivolumab for up to 12 months and have 2 consecutive tumor assessments confirming Complete response (CR), Partial response (PR), or Stable disease (SD)

AML that has failed to achieve complete remission or morphologic complete remission or

History of at least one anti-CD20 antibody containing regimen that resulted in initial measurable response (partial or complete remission), followed by relapse/recurrence.

Documented major response [partial response (PR), very good partial response (VGPR), complete response (CR)] according to the International Myeloma Working Group (IMWG) uniform response criteria, version 2011, after this initial therapy.

Patients must have received at least one prior therapy for CLL or NHL, need additional treatment (or have need for cytoreduction as mentioned above), and meet criteria for relapsed or refractory disease; they may not be a candidate for curative therapy; relapsed disease is defined as a patient who previously achieved a complete remission (CR) or a partial remission (PR), but after a period of six or more months demonstrates evidence of disease progression; refractory disease is defined as progression within six months of the last anti-leukemic or anti-lymphoma therapy, or any response less than a CR or PR

MDS/CMML, relapsed from, or refractory to, prior HMA therapy; the latter defined as failure to achieve clinical remission (CR), partial remission (PR) or hematologic improvement (HI) after previous HMA therapy (? 4 cycles of azacitidine or decitabine), or progression during, or toxicity to previous HMA therapy precluding further HMA treatment, and,

Patients with HD with 4th or greater CR, PR, and/or SD are ineligible.

Creatinine (Cr) > 1.5 mg/dL or Cr clearance < 60 mL/m^2

Subjects must have histologically documented acute myeloid leukemia (AML), acute lymphoblastic leukemia (ALL), myelodysplastic syndrome (MDS), myeloproliferative disorders (MPD), chronic myeloid leukemia (CML), non-Hodgkin lymphoma (NHL), Hodgkin lymphoma (HL) or multiple myeloma (MM) as follows:\r\n* Acute myeloid leukemia (AML) with one or more of the following criteria:\r\n** Poor risk cytogenetics, including -5, 5q-, -7, 7q-, t(9;22); complex cytogenetics (>= 3 abnormalities); or normal cytogenetics with Fms-like tyrosine kinase 3 (Flt3) internal tandem duplications (ITD), in first or subsequent complete remission (CR)\r\n** Relapsed or primary refractory AML with =< 10% blasts in the peripheral blood\r\n** Subjects in CR1 who required two cycles of induction to achieve remission may be included at the discretion of the treating physician\r\n** Standard risk or intermediate risk cytogenetics in second or subsequent CR (enrolled at the discretion of the treating physician)\r\n* Acute lymphoblastic leukemia (ALL) with one of the following criteria:\r\n** Second or subsequent CR\r\n** Any partial remission (PR) (no circulating blasts)\r\n** High-risk ALL in first CR including (Philadelphia chromosome positive [Ph+], t(4:11)), complex karyotype, hypodiploidy (< 44 chromosomes), positive minimal residual disease (MRD) after induction, and other high risk features in adults per treating physician\r\n* Myelodysplasia, intermediate-2 (score 1.5-2.0) or high risk (score > 2.5) by the International Prognostic Score System\r\n* Myeloproliferative disorders (include chronic myelomonocytic leukemia [CMML], agnogenic myeloid metaplasia [AMM] or idiopathic myelofibrosis, and juvenile myelomonocytic leukemia [JMML]) with excess blasts (> 5%)\r\n* Chronic myeloid leukemia (CML) with one of the following criteria:\r\n** Second or subsequent chronic phase\r\n** Accelerated phase\r\n** Blast crisis\r\n* Non-Hodgkin's lymphoma (NHL) meeting one of the following criteria:\r\n** Relapse after autologous stem cell transplantation with evidence of responsive disease\r\n** Subject with chemosensitive relapse who have no option for autologous stem cell transplantation due to blood or marrow involvement or failure to mobilize autologous stem cells or are not considered eligible for autologous transplant by their treating physician\r\n* Hodgkin’s lymphoma: relapse after autologous hematopoietic cell transplant (HCT), chemorefractory disease\r\n* Multiple myeloma: per National Comprehensive Cancer Network (NCCN) guidelines

Acute myeloid leukemia, including biphenotypic acute leukemia or mixed-lineage leukemia:\r\n* All patients must be in CR as defined by hematologic recovery and < 5% blasts by morphology/flow cytometry in a representative bone marrow sample with cellularity >= 15% for age; patients who do not have high-risk features (for example preceding myelodysplastic syndrome [MDS], high-risk cytogenetics, >= 2 cycles to obtain CR, erythroblastic or megakaryocytic leukemia or >= CR2) must be discussed with the principal investigator (PI) prior to enrollment and at the Patient Care Conference or equivalent group such as the pediatric leukemia board as an alternative\r\n* Patients in whom adequate marrow/biopsy specimens cannot be obtained to determine remission status by morphologic assessment, but have fulfilled criteria of remission by flow cytometry, recovery of peripheral blood counts with no circulating blasts, and/or normal cytogenetics (if applicable) may still be eligible; reasonable attempts must be made to obtain an adequate specimen for morphologic assessment, including possible repeat procedures; these patients must be discussed with the PI prior to enrollment; patients persistently aplastic for greater than one month since completing last chemotherapy are also eligible with PI approval

Acute lymphoblastic leukemia, including biphenotypic acute leukemia or mixed-lineage leukemia:\r\n* All patients must be in CR as defined by < 5% blasts by morphology; flow cytometry in a representative bone marrow sample with cellularity >= 15% for age; patients who do not have high-risk disease (high risk CR1, greater than one cycle to obtain CR or >= CR2) must be discussed with the PI prior to enrollment and at the Patient Care Conference or equivalent group such as the pediatric leukemia board as an alternative\r\n* Patients in whom adequate marrow/biopsy specimens cannot be obtained to determine remission status by morphologic assessment, but have fulfilled criteria of remission by flow cytometry, recovery of peripheral blood counts with no circulating blasts, and/or normal cytogenetics (if applicable) may still be eligible; reasonable attempts must be made to obtain an adequate specimen for morphologic assessment, including possible repeat procedures; these patients must be discussed with the principal investigator Ann Dahlberg prior to enrollment; patients persistently aplastic for greater than one month since completing last chemotherapy are also eligible with PI approval

Mantle-cell lymphoma, prolymphocytic leukemia: Eligible after initial therapy in >= CR1 or >= PR1

Large cell NHL > CR2/> second partial response (PR2):\r\n* Patients in CR2/PR2 with initial short remission (< 6 months) are eligible\r\n* These patients must be presented at PCC prior to enrollment, given potential competing eligibility on autotransplant protocols

For AML: patients must belong to one of the following ‘high risk’ categories: \r\n* Primary induction failure (PIF) as defined by failure to achieve at least a 50% reduction in bone marrow blasts after one cycle of high intensity, anthracycline containing induction regimen or failure to achieve complete response (CR)/complete remission with incomplete blood count recovery (CRi) after two cycles of high intensity chemotherapy\r\n* First early relapse as defined by an initial remission duration of fewer than 6 months\r\n* Second or subsequent relapse regardless of remission duration, or\r\n* Relapse after allogeneic or autologous stem cell transplantation (first relapse after stem cell transplant would be eligible, regardless of prior duration of remission)

For ALL: patients must belong to one of the following ‘high risk’ categories: \r\n* Primary refractory as defined by failure to achieve CR after induction and at least one salvage therapy \r\n* Second or subsequent relapse \r\n* Relapse after allogeneic or autologous stem cell transplantation (requirement for second relapse does not apply post-transplant) \r\n* All variants of ALL including T-ALL, B / myeloid, lymphoblastic leukemia lymphoma are eligible

Patients with newly diagnosed, previously untreated B-lineage ALL, or having achieved complete remission (CR) with one course of induction chemotherapy

This study is open to patients with acute myeloid leukemia (AML) evaluated within 30 days of the start of conditioning regimen and in first or second complete remission (CR)

Patients with B-lineage ALL in hematologic complete remission (CR) with molecular failure (ie, had never achieved an MRD-negativity status before inotuzumab ozogamicin) or had a molecular relapse (i.e., became MRD positive after having been MRD negative) starting at any time point after 3 months of frontline therapy. Molecular disease or minimal residual disease is defined by a value of at least of 10^-4 by multicolor flow cytometry

Patients with B-lineage ALL in CR2 and beyond with molecular failure at any time point after 2 months of salvage therapy are allowed

Acute myelogenous leukemia (AML):\r\n* Complete first remission (CR1) at high risk for relapse such as any of the following:\r\n** Known prior diagnosis of myelodysplasia (MDS) or myeloproliferative disorder.\r\n** Therapy-related AML.\r\n** White cell count at presentation > 100,000.\r\n** Presence of extramedullary leukemia at diagnosis.\r\n** Any unfavorable subtype by French-American-British (FAB) or World Health Organization (WHO) classification.\r\n** High-risk cytogenetics (e.g. those associated with MDS, abnormalities of 5, 7, 8, complex karyotype) or high risk molecular abnormalities.\r\n** Requirement for 2 or more inductions to achieve CR1.\r\n** Any patient with newly diagnosed AML with intermediate risk cytogenetics who elects allograft with curative intent over consolidation chemotherapy.\r\n** Any patient unable to tolerate consolidation chemotherapy as would have been deemed\r\nappropriate by the treating physician.\r\n** Other high risk features not defined above.\r\n* Complete second remission (CR2).\r\n* Primary refractory or relapsed AML with less than 10% blasts before transplant. Persistent/relapsed AML with cytogenetic, flow cytometric, or molecular aberrations in >= 10% of cells are eligible.

Acute lymphoblastic leukemia (ALL):\r\n* Complete first remission (CR1) at high risk for relapse such as any of the following:\r\n** White cell count at presentation > 30,000 for B-cell lineage and > 100,000 for T-cell lineage.\r\n** Presence of any high-risk cytogenetic abnormalities such as t(9;22), t(1;19), t(4;11) or other MLL rearrangements (11q23) or other high-risk molecular abnormality.\r\n** Failure to achieve complete remission after four weeks of induction therapy.\r\n** Persistence or recurrence of minimal residual disease on therapy.\r\n** Any patient with newly diagnosed ALL >= 50 years-old.\r\n** Any patient unable to tolerate consolidation and/or maintenance chemotherapy as would have been deemed appropriate by the treating physician.\r\n** Other high risk features not defined above.\r\n* Complete second remission (CR2).\r\n* Primary refractory or relapsed ALL with less than 5% blasts before transplant. Persistent/relapsed ALL with cytogenetic, flow cytometric or molecular aberrations in >= 5% of cells are eligible.

On treatment with ruxolitinib for at least 3 months and have been on a stable dose for at least 8 weeks and have not achieved a complete response (CR) by International Working Group (IWG) criteria

First relapse if first remission ? 12 months

Patients must have received treatment on PBTC-029 or PBTC-029B for a minimum of 12 courses with at least stable disease, or had a sustained response (partial response [PR]/ complete response [CR]) but remained on treatment < 12 courses

Absence of a documented partial response (PR) or complete response (CR) according to RECIST 1.1 or CA 125 response by Gynecologic Cancer Intergroup (GCIG) criteria to neoadjuvant chemotherapy

Patients with the following hematologic malignancies:\r\n* Acute myelogenous leukemia (AML): High-risk AML including:\r\n** Antecedent hematological disease (e.g., myelodysplasia [MDS])\r\n** Treatment-related leukemia\r\n** Complete remission (CR1) with poor-risk cytogenetics or molecular markers (e.g. Flt 3 mutation, 11q23, del 5, del 7, complex cytogenetics)\r\n** CR2 or CR3\r\n** Induction failure or 1st relapse with =< 10% blasts in the marrow\r\n* Acute lymphoblastic leukemia (ALL)\r\n** High-risk CR1 including:\r\n*** Poor-risk cytogenetics (e.g., Philadelphia chromosome t(9;22) or 11q23 rearrangements)\r\n*** Presence of minimal disease by flow cytometry after 2 or more cycles of chemotherapy\r\n** No CR within 4 weeks of initial treatment\r\n** Induction failure with =< 10% blasts in the marrow\r\n** CR2 or CR3\r\n* Myelodysplastic syndromes (MDS), intermediate, high or very high risk by the revised international prognostic scoring system (IPSS-R)\r\n* Chronic myelogenous leukemia (CML) in second chronic phase after accelerated or blast crisis\r\n* Myelofibrosis (MF):\r\n** Intermediate-2 or high risk by Dynamic International Prognostic Scoring System (DIPSS)-plus OR\r\n** Monosomal karyotype OR\r\n** Presence of inv(3)/i(17q) abnormalities OR\r\n** Other unfavorable karyotype OR leukocytes >= 40 x 10(9)/L AND\r\n** Circulating blasts =< 9%\r\n* Relapsed or refractory lymphoid malignancies (including non-Hodgkin lymphoma, Hodgkin lymphoma) meeting the following criteria:\r\n** Disease status: Stable disease, partial remission or 2nd and 3rd complete remission\r\n** Have relapsed after autologous transplant or who have failed to collect for an autologous transplant

Disease response noted (i.e. CR, non-CR, or not applicable): assessed as per disease specific criteria

Relapsed or refractory (resistant) disease, as defined by standard criteria\r\n* Relapsed: Bone marrow blasts >= 5%, reappearance of blasts in the blood, or development of extramedullary disease following achievement of complete remission (CR)/complete remission with incomplete recovery of blood counts (CRi)/complete remission with incomplete recovery of platelets (CRp)/morphologic leukemia free state (MLFS)\r\n* Refractory (resistant): Failure to achieve CR/CRi/MLFS in subjects who survive >= 7 days following completion of initial treatment, with evidence of persistent leukemia by blood and/or bone marrow examination

Diagnosis of one of the following: a): Patients >= 60 years of age with previously untreated Ph-positive ALL [either t(9;22) and/or BCR-ABL positive] (includes patients initiated on first course of therapy before cytogenetics known): This patient could have received one or two courses of chemotherapy with or without other tyrosine kinase inhibitors (TKIs) and still eligible; b) If they achieved CR, they are assessable only for event-free and overall survival; or c) If they failed to achieve CR, they are assessable for CR, event-free, and overall survival; d) Patients >= 18 years of age with relapsed/refractory Ph-positive ALL.

Mantle cell NHL-may be treated in first complete remission (CR); (diagnostic lumbar puncture [LP] required pre-transplant)

For B-ALL\r\n* Chemotherapy refractory disease in subjects with B-ALL is defined as progression or stable disease after two lines of lines of therapies\r\n* Recurrence of disease after achieving complete remission (CR)\r\n* Subjects with persistent or relapsed minimal residual disease (MRD) (by flow cytometry, polymerase chain reaction [PCR], fluorescence in situ hybridization [FISH], or next generation sequencing) require verification of MRD positivity on two occasions at least 4 weeks apart\r\n* Subjects with Philadelphia chromosome positive acute lymphoblastic leukemia (Ph+ALL) subjects are eligible if they progressed, had stable disease or relapsed after two lines of therapy, including tyrosine kinase inhibitors (TKIs)\r\n* Subjects with recurrence of isolated central nervous system (CNS) relapse after achieving complete remission (CR); if relapsed with MRD, will require verification of MRD positivity on two occasions at least 4 weeks apart

Previous tumor response to PD-1 or PD-L1 inhibiting therapy\r\n* Note: Tumor response is defined as complete response (CR), partial response (PR), or stable disease (SD) that is durable for at least 16 weeks

Patients must have a history of tumor progression or relapse or failure to achieve complete response following standard high-dose induction chemotherapy

Patients with complete response (CR)/very good partial response (VGPR) disease

Inclusion Criteria:\n\n        AML confirmed subjects aged ? 60 years who have achieved complete remission (CR or CRi)\n        after induction/consolidation Ara-C based therapy, that have MRD positive status and are\n        not planned for stem cell transplantation.\n\n        Exclusion Criteria:\n\n        Subjects diagnosed with acute promyelocytic leukemia or with extramedullary AML or subjects\n        who have achieved CR or CRi following treatment for AML. Subjects who have received\n        treatment with hypomethylating agents.

Patients >= 60 years of age with previously treated Ph-positive ALL, after 1-2 courses of chemotherapy with or without other tyrosine kinase inhibitors (TKIs). If they achieved CR, they are assessable only for event-free and overall survival, or If they failed to achieve CR, they are assessable for CR, event-free, and overall survival.

Patients without evidence of documented disease progression clinically or radiographically after ASCT (stable disease [SD], partial remission [PR] or complete remission [CR]) who have had count recovery (absolute neutrophil count [ANC] > 500 cells/mm^3, non-transfused platelet count > 20,000 K/mm^3) and are at least 30 days post ASCT but no more than 120 days post ASCT

Patients must have advanced AML, ALL or high-risk MDS meeting one of the following descriptions:\r\n* AML or ALL beyond first remission (i.e., having relapsed at least one time after achieving remission in response to a treatment regimen)\r\n* AML or ALL representing primary refractory disease (i.e., having failed to achieve remission at any time following one or more prior treatment regimens)\r\n* AML evolved from myelodysplastic or myeloproliferative syndromes\r\n* MDS expressed as refractory anemia with excess blasts (RAEB)\r\n* Chronic myelomonocytic leukemia (CMML) by French-American-British (FAB) criteria

Patients not in remission must have CD45-expressing leukemic blasts; patients in remission do not require phenotyping and may have leukemia previously documented to be CD45 negative

Patients with active (blood or bone marrow blasts > 5%) relapsed or refractory CD33+ acute myeloid leukemia (AML) de novo, or secondary. a. Relapsed AML is defined as patients that had a first complete remission (CR) before developing recurrent disease. b. Refractory AML defined as patients that have not achieved a CR after 2 cycles of induction chemotherapy.

Patients in partial or complete remission following cell therapy will also be eligible

NHL patients with resistant or refractory lymphoma (no partial remission [PR] following up to three cycles of combination chemotherapy) will not be eligible for transplant in this trial

Lymphoblastic lymphoma\r\n* All patients will be eligible in second or greater complete remission (CR) or first or subsequent partial remission (PR)\r\n* Patients with any high-risk features will be eligible in first complete remission\r\n* High risk features include:\r\n** Stage IV\r\n** Lactate dehydrogenase (LDH) > 2 x upper limit of normal\r\n** >= 2 extranodal sites

Mature T-cell lymphoma\r\n* Chemosensitive T-cell lymphomas including primary T-cell not otherwise specified angioimmunoblastic, and ALK-positive anaplastic large cell, will be eligible after initial therapy, whether or not CR is achieved\r\n* Mycosis fungoides/Sezary syndrome will be eligible in >= CR2/PR2

For stage I/II patients treated with primary chemotherapy-radiation, they must have failed (no CR or progression after CR) at least one salvage combination chemotherapy treatment regimen

PHASE I: Patients who have/are either:\r\n* Transplanted in hematologic first complete remission with evidence of minimal residual disease within 45 days of allogeneic transplantation\r\n** Pre- or post-transplant minimal residual disease defined by:\r\n*** Any detectable acute lymphocytic leukemia (ALL) (by flow cytometry, cytogenetics, or polymerase chain reaction [PCR] techniques) as per clinical indication\r\n* In second or third complete remission at the time of allogeneic transplantation\r\n* Treated with reduced intensity regimens\r\n* Lymphoid blast crisis of chronic myelogenous leukemia (CML)\r\n* Are relapsed or refractory to at least 1 line of chemotherapy

PHASE II: Patients who have/are either:\r\n* Transplanted in hematologic first complete remission with evidence of minimal residual disease within 45 days of allogeneic transplantation\r\n** Post-Transplant Minimal Residual Disease defined by:\r\n*** Any detectable ALL (by flow cytometry, cytogenetics, or PCR techniques) as per clinical indication\r\n* In second or third complete remission at the time of allogeneic transplantation\r\n* Treated with reduced intensity regimens\r\n* Lymphoid blast crisis of CML\r\n* Are relapsed or refractory to at least 1 line of chemotherapy

Pediatric patients with acute lymphoblastic leukemia (ALL) that is t (9,22) positive in first remission are not eligible unless there is evidence of minimal residual disease after initial induction and/or consolidation treatment or the pediatric Philadelphia chromosome positive (Ph+) ALL is clinically refractory to available therapies with evidence of persistence in the bone marrow or peripheral blood.

Diagnosis of acute myeloid leukemia (AML) and meets one of the following disease criteria:\r\n* Primary induction failure:\r\n** De Novo AML: No CR after 2, 3 or 4 induction attempts with high dose chemotherapy\r\n** Secondary AML (from myelodysplastic syndrome [MDS] or treatment related): No CR after 1, 2 or 3 cycles of high dose chemotherapy\r\n* Relapsed:\r\n** Not in CR after 1 or 2 cycles of standard re-induction therapy\r\n*** For patients > 60 years of age, the minimum of 1 cycle of standard chemotherapy is not required

Chemo-sensitive (defined by complete response [CR] or partial response [PR] to most recent chemo regimen) based on pre-transplant positron emission tomography (PET) within 6 weeks of autologous transplant

Diagnosis of acute myeloid leukemia (AML) and meets one of the following disease criteria:\r\n* Primary induction failure:\r\n** De novo - no CR after 2 or more induction attempts with high dose chemotherapy\r\n** Secondary AML (from myelodysplastic syndrome [MDS] or treatment related): no CR after 1 or more cycles of high dose chemotherapy\r\n** Note: hypomethylating agents such as azacitidine will count as induction failure\r\n* Relapsed: not in CR after 1 or more cycles of standard re-induction therapy - patients > 60 years of age, the 1 cycle of standard chemotherapy is not required\r\n* Relapsed > 18 months after transplant: no re-induction required and no more than 1 re-induction cycle is allowed

Achieved either partial or CR to the bendamustine regimen of at least 12 months in duration before relapse/progression.

Patients must be in first CR/VGPR

Relapsed disease defined as complete remission to first-line therapy followed by biopsy-proven relapse ? 12 months of initiating first-line therapy

Patients must have: a. Relapsed and/or refractory non-APL AML that has failed to achieve a complete remission (CR) or partial remission (PR) following standard induction therapy, or has relapsed after any duration of CR or PR i. Patients must have measurable disease with bone marrow blasts ?5%at screening b. Relapsed and/or refractory higher-risk MDS (High / Very High Risk, as defined by the Revised International Prognostic Scoring System (IPSS-R)) that has failed to achieve a CR or PR, or any hematologic improvement (HI, per IWG 2006 criteria) after standard therapy with hypomethylating agents (e.g., azacitidine, decitabine), or has relapsed after any duration of CR or PR or HI i. Patients must have measurable disease with bone marrow blasts >5% at screening c. Newly diagnosed, treatment-naïve non-APL AML in patients who, at the time of study entry are unlikely to tolerate standard intensive chemotherapy due to age, performance status, or comorbidities based on at least one of the following criteria (Ferrara et al, 2013): i. Age ? 75 years old ii. Eastern Cooperative Oncology Group (ECOG) Performance Status (PS) of 3 iii. Cardiac history of congestive heart failure (CHF) or documented ejection fraction (EF) ? 50% iv. Pulmonary disease with DLCO ? 65% or FEVI ? 65% v. Creatinine clearance ? 30 mL/min to < 45 mL/min vi. Hepatic impairment with total bilirubin > 1.5 to ? 3.0 x upper limit of normal (ULN) vii. Any other comorbidity that the Investigator judges to be incompatible with intensive chemotherapy, and reviewed and approved by the Sponsor prior to enrollment d. Transfusion dependent lower-risk MDS without the del 5q abnormality, in patients refractory to erythropoietin treatment or unlikely to respond to erythropoietin treatment (EPO >500). i. Lower-risk MDS: Very Low /Low / Intermediate Risk, as defined by IPSS-R. ii.Red blood cell (RBC) transfusion dependent anemia defined as no eight consecutive weeks without RBC transfusions within the 16 weeks prior to study entry, or ?4 RBC transfusions within the 8 weeks prior to study entry. iii.Refractory to or ineligible for ESAs is defined as RBC-Transfusion Dependence despite ESA treatment of ?40,000 units/week recombinant human erythropoietin for 8 weeks or an equivalent dose of darbepoetin (150 µg/week) or serum EPO level >500 mU/mL in patients not previously treated with ESAs.

Patients must be either refractory to or relapsed after only induction therapy; patients who do not achieve CR after induction therapy are considered primary refractory and are allowed to enter study

Acute myeloid leukemia (AML): second or greater complete remission (CR); first CR (CR1) in patients >= 60 years old; CR1 in < 60 years old that is NOT considered as favorable risk\r\n* Favorable risk AML is defined as having one of the following:\r\n* t(8,21) without cKIT mutation\r\n* inv(16) or t(16;16) without cKIT mutation\r\n* Normal karyotype with mutated NPM1 but FLT3-ITD wild type\r\n* Normal karyotype with double mutated CEBPA\r\n* Acute prolymphocytic leukemia (APL) in first molecular remission at the end of consolidation

Acute lymphoblastic leukemia (ALL)/lymphoma: second or greater CR; CR1 unable to tolerate consolidation chemotherapy due to chemotherapy-related toxicities; CR1 high-risk ALL; high risk ALL is defined as having one of the following:\r\n* Evidence of high risk cytogenetics, e.g. t(9;22), t(1;19), t(4;11), other MLL rearrangements, IKZF1\r\n* Recipient age 30 years and older at diagnosis\r\n* White blood cell counts of greater than 30,000/mcL (B-ALL) or greater than 100,000/mcL (T-ALL) at diagnosis\r\n* Central nervous system (CNS) leukemia involvement during the course of disease \r\n* Slow cytologic response (> 10% lymphoblasts in bone marrow on day 14 of induction therapy)\r\n* Evidence of persistent immunophenotypic or molecular minimal residual disease (MRD) at the end of induction and consolidation therapy

Biphenotypic/undifferentiated/prolymphocytic leukemias in first or subsequent CR

Burkitt’s lymphoma in CR2 or subsequent CR

Relapsed T-cell lymphoma that is chemotherapy sensitive in CR/partial response (PR) that has failed or ineligible for an autologous transplant

Acute lymphocytic leukemia (ALL) in complete remission (CR)1 with high-risk features including adverse cytogenetic such as t(9;22), t(1;19), t(4;11), or MLL gene rearrangements; in second or greater morphologic remission; persistent minimal residual disease

Acute myeloid leukemia (AML) in CR1 with intermediate-risk disease and persistent detectable minimal residual disease (MRD), or with high-risk features defined as: greater than 1 cycle of induction therapy required to achieve remission; preceding myelodysplastic syndrome (MDS) or myeloproliferative disease; presence of FLT3 mutations or internal tandem duplications, DNMT3a, TET2, MLL-partial tandem duplication (PTD), ASXL1, PHF6; FAB M6 or M7 classification; adverse cytogenetics including: -5, del 5q, -7, del7q, abnormalities involving 3q, 9q, 11q, 20q, 21q, 17, +8, complex [> 3 abnormalities]

Participants who have had a complete response (CR) after pre-study therapy are not eligible for study

Pathological confirmation by bone marrow documenting the following:\r\n* Acute myeloid leukemia (AML) which has relapsed after complete remission\r\n* AML which has been refractory to two prior induction attempts\r\n* Acute lymphoblastic leukemia (ALL) which has relapsed after complete remission\r\n* ALL which has been refractory to two prior induction attempts

Subjects with acute myeloid leukemia (AML) should have failed any prior induction therapy regimen or have relapsed after prior therapy (defined as patients in first relapse and less than 12 months from diagnosis [short first remission] or in second or later relapse; refractory defined as failure to achieve complete response [CR] to standard induction therapy, such as \7 and 3\, high dose ara-C-containing regimen or a hypomethylating agent): dose-escalation phase: subjects with confirmed relapsed or refractory AML and no available treatment options with known benefit; expansion phase: subjects with relapsed/refractory AML who have failed therapy with up to one prior salvage regimen and no available treatment options with known benefit; exception: stem cell transplant (SCT) or stem cell therapy for subjects who previously underwent SCT/stem cell therapy, and are currently in remission will not be considered a salvage regimen

Acute lymphoid leukemia (ALL) in first complete remission (CR1) with high risk for relapse including:\r\n* t(9;22) or detected BCR-ABL1 translocation by genomic methodologies\r\n* BCR-ABL1-Like B-ALL including mutations of IKZF1 or CRLF2\r\n* Translocations or mutations involving 11q23 (MLL) gene\r\n* Hypodiploid karyotype\r\n* Deletion of 9p\r\n* Loss of 17p or TP53 mutation\r\n* T-lymphocyte lineage antigen expression (T-ALL)\r\n* Central nervous system (CNS) or other extramedullary involvement\r\n* White blood cell (WBC) count >= 100,000 cells/uL at diagnosis

Patients with newly diagnosed, previously untreated B-lineage ALL or lymphoblastic lymphoma, or having achieved complete remission (CR) with one course of induction chemotherapy; patients who require steroids, cytarabine (ara-c) or hydrea to manage disease symptoms prior to finalization of diagnosis and treatment plan are allowed and eligible

Patients with complete response (CR) or stringent CR after induction therapy as defined by International Response Criteria after most recent therapy

Patients with B-lineage ALL in a) hematologic complete remission (CR) beyond CR1 at time of transplant; patients beyond CR1 or with primary induction failure may be without minimal residual disease, b) any residual disease defined by positive flow > 0.01%, detection of breakpoint cluster region-abelson murine leukemia viral oncogene homolog 1 (BCR-ABL) transcript by polymerase chain reaction (PCR) with a sensitivity of 1/10,000, or detection of the t(9;22) translocation in any metaphases by cytogenetics at time of transplant, or presence of the MLL gene

Refractory AML without complete remission (CR) after 2 or more cycles of induction therapy (primary induction failure), or AML relapsed after obtaining a CR and failed one cycle of re-induction therapy; standard dose 10-day decitabine (20 mg/m^2 daily IV x 10 days) or 7-day azacitidine (75-100 mg/m^2 daily SC/IV x 7 days) will be considered as one cycle of induction therapy

Patients who achieved complete response (CR) prior to autologous HCT

Response to therapy and completion of at least one cycle of consolidation therapy, and with disease status meeting one of the following criterion at the time of post-induction disease restaging:\r\n* Minimal residual disease, as defined by detectable disease by flow cytometry but with marrow that is at least 10% cellular with < 5% blasts on morphologic review\r\n* Complete remission with incomplete blood count recovery (CRi)/complete remission with incomplete platelet recovery (CRp), as defined by absence of detectable disease by flow cytometry, and marrow that is at least 10% cellular with < 5% blasts on morphologic review, but with neutrophil count < 1000/ul (CRi) and/or platelet count < 100,000/ul (CRp); in pediatric patients, a platelet threshold of < 80,000/ ul will be used, as per consensus pediatric response criteria

Continued CR, CRp, or CRi within 3 weeks of first dose WT-1 specific CD8+ T cells

In a morphologic complete remission with incomplete blood count recovery, or morphologic complete remission post-induction after no more than 2 induction cycles

Relapse after minimal residual disease (MRD)-negative CR within 3 months of most recent GCLAM chemotherapy

Acute lymphoblastic leukemia (ALL): Induction failure, primary refractory to treatment (do not achieve complete remission after first course of therapy) or are beyond first remission including second or greater remission or active disease; patients in first remission are eligible if they are considered high risk, defined as any of the following detected at any time: with translocations 9;22 or 4;11, hypodiploidy, complex karyotype, secondary leukemia developing after cytotoxic drug exposure, and/or evidence of minimal residual disease or acute biphenotypic leukemia, or double hit non-Hodgkin's lymphoma

Hodgkin's disease (HD): Induction failures, after first complete remission, or relapse (including relapse post autologous hematopoietic stem cell transplant), or those with active disease

Acute myeloid leukemia (AML) and related precursor neoplasms: 2nd or greater complete remission (CR); first complete remission (CR1) in patients > 60 years old; CR1 in =< 60 years old that is NOT considered as favorable-risk; favorable risk AML is defined as having one of the following:\r\n* t(8,21) without cKIT mutation\r\n* inv(16) or t(16;16) without cKIT mutation \r\n* Normal karyotype with mutated NPM1 and wild type FLT-ITD\r\n* Normal karyotype with double mutated CEBPA\r\n* Acute prolymphocytic leukemia (APL) in first molecular remission at the end of consolidation

Acute lymphoblastic leukemia (ALL)/lymphoma: second or greater CR; CR1 unable to tolerate consolidation chemotherapy due to chemotherapy-related toxicities; CR1 high-risk ALL; high risk ALL is defined as having one of the following:\r\n* Evidence of high risk cytogenetics, e.g. t(9;22), t(1;19), t(4;11), other MLL rearrangements, IKZF1\r\n* 30 years of age or older at diagnosis\r\n* White blood cell counts of greater than 30,000/mcL (B cell [B]-ALL) or greater than 100,000/mcL (T cell [T]-ALL) at diagnosis\r\n* Central nervous system (CNS) leukemia involvement during the course of disease\r\n* Slow cytologic response (> 10% lymphoblasts in bone marrow on day 14 of induction therapy)\r\n* Evidence of persistent immunophenotypic or molecular minimal residual disease (MRD) at the end of induction and consolidation therapy

Biphenotypic/undifferentiated/prolymphocytic leukemias in first or subsequent CR

Minimal residual disease (MRD) positive leukemia (AML, ALL or accelerated/blast phase CML); selected patients in morphologic CR, but with positive immunophenotypic (flow cytometry) or molecular evidence of MRD may be eligible if recent chemotherapy has not resulted in MRD negative status

Burkitt’s lymphoma in CR2 or subsequent CR

Relapsed T-cell lymphoma that is chemotherapy sensitive in CR/partial remission (PR) that has failed or ineligible for an autologous transplant

Plasma Cell Leukemia after initial therapy if achieved at least in partial remission; or relapsed and achieved subsequent remission (CR/PR)

Presence of measurable or evaluable disease (unless patient has achieved a complete response (CR) following first-line antineoplastic therapy).

Patients without measurable or evaluable disease (unless patients achieved a complete response (CR) following 1st-line antineoplastic therapy).

Have a newly diagnosed AML, based on World Health Organization criteria, currently in first (1st) complete remission (CR)/complete remission with incomplete count recovery (CRi) on a bone marrow biopsy performed within 4 weeks of study enrollment

Cohort 3: High risk AML and MDS patients who are in complete remission morphologically with no evidence of minimal residual disease by flow cytometry or cytogenetic or molecular testing after allogeneic stem cell transplantation

Patient relapsing more than 2 years after initial remission

Acute myeloid leukemia: High risk first complete remission (CR1) (as evidenced by preceding myelodysplasia [MDS], high risk cytogenetics, >= 2 cycles to obtain CR, erythroblastic or megakaryocytic leukemia, FLT-3 ITD +; second or higher complete response [CR2+]); all patients must be in CR as defined by hematological recovery, AND < 5% blasts by light microscopy within the bone marrow with a cellularity of >= 15%

Acute lymphocytic leukemia (ALL): Factor that define high risk CR1 include but are not limited to cytogenetics demonstrating t(9;22), t (1:19), t(4;11), other MLL rearrangements, hypodiploidy, or IKZF1 abnormalities), DNA index < 0.81, > 1 cycle to obtain CR or presence minimal residual disease (MRD); patients in CR2+ are eligible; all patients must be in CR as defined by hematological recovery, AND < 5% blasts by light microscopy within the bone marrow with a cellularity of >=15%

Very high risk pediatric patients with ALL: Patients < 21 years are also considered high risk CR1 if they had M2 or M3 marrow at day 42 from the initiation of induction or M3 marrow at the end of induction; they are eligible once they achieved a complete remission

Large cell non-Hodgkin lymphoma (NHL) > CR2/> PR2: Patients in CR2/PR2 with initial short remission (< 6 months) are eligible

Patients with complete response (CR)/very good partial response (VGPR) disease

Patients must have a sustained clinical response (PR, nodular PR [nPR], complete clinical response [CCR], CR with incomplete marrow recovery [CRi], CR) with documented residual disease (>= 1 CLL cell per 10,000 leukocytes or >= 0.01% MRD) either in the blood, bone marrow or a lymph node >= 3.5 cm by any available techniques

Patients must be currently receiving ibrutinib for at least 6 months prior to enrollment in the study and:\r\n* Not experiencing any >= grade 2 non-hematologic ibrutinib-related toxicity\r\n* The best response to ibrutinib therapy must not have exceeded partial response or stable disease (i.e. no complete response [CR] or complete response with incomplete marrow recovery [CRi])\r\n* Note: patients carrying a deletion at chromosome 17p (i.e. deletion [del][17p]), and/or tumor protein (TP)53, Bruton's tyrosine kinase (BTK), and at the phospholipase C, gamma 2 (PLCgamma 2) loci mutations, will be eligible if they are receiving frontline therapy with ibrutinib

Relapsed or refractory B-cell ALL:\r\n* 1st or greater bone marrow (BM) relapse OR\r\n* Any marrow relapse after allogeneic hematopoietic stem cell transplantation (HSCT) and > 100 days from transplant OR\r\n* For patients with refractory disease:\r\n** < 60 years old that have not achieved a complete remission (CR) after > 2 or more chemotherapy regimens\r\n** >= 60 years old that have not achieved a CR after 1 prior chemotherapy regimen

Participants who received at least only one line of previous therapy and achieved either complete response (CR) or partial response (PR) for at least 24 weeks (from the last day of the last cycle) after their first line of therapy, but are not eligible for high dose chemotherapy with autologous stem cell transplantation (HD-ASCT)

Participants who received more than one line of previous therapy (including HD-ASCT), and have achieved a duration of response (CR or PR) of at least 8 weeks (from the last day of the last cycle) after their last line of therapy

First relapsed participants aged less than (<) 60 years with first CR duration greater than (>) 1 year

Patients with AML in remission (defined as CR, CR with incomplete platelet recovery –CRp-, CR with incomplete hematologic recovery -CRi-, or partial remission defined as a bone marrow with < 10% blasts after therapy with or without hematologic recovery)

Patients must meet one of the three treatment history criteria:\r\n* Relapsed AML who have failed at least 1 line of salvage therapy\r\n* De novo AML who have not achieved CR after 2 lines of therapy\r\n* AML evolving from myelodysplastic syndrome (MDS) or myeloproliferative disorder who have failed hypomethylating agent or induction chemotherapy\r\n* Patients who have relapsed after allogeneic hematopoietic cell transplant (HCT) are eligible if they are at least 3 months after HCT, do not have active graft vs. host disease (GVHD) and are off immunosuppression except for maintenance dose of steroids (prednisone 10 mg/day or less)

Hematologic Malignancy\r\n* No human leukocyte antigen (HLA) identical sibling or suitable unrelated donor, or time needed to find an acceptable unrelated donor match would likely result in disease progression such that the patient may become ineligible for any type of potentially curative transplant\r\n* Relapsed or primary therapy-refractory acute myeloid leukemia (AML) with bone marrow blast < 20%\r\n* High-risk refractory or relapsed acute lymphoblastic leukemia (ALL) in patients for whom transplantation is deemed indicated (relapse occurring < 30 months from diagnosis, patients relapsing after previous allogeneic transplant, relapse after 2nd remission, primary induction failure or hypodiploidy)\r\n* Patients with relapsed Hodgkin lymphoma unable to achieve 2nd remission or very good partial remission (VGPR) and therefore ineligible to receive autologous stem cell transplantation\r\n* Patients with Hodgkin lymphoma relapsing after autologous stem cell transplant\r\n* Patients with primary refractory or relapsed non-Hodgkin lymphoma (NHL) unable to achieve 2nd remission or very good partial remission (VGPR) and therefore ineligible to receive autologous stem cell transplantation\r\n* Patients with NHL relapsing after autologous stem cell transplant\r\n* Patients with myelodysplastic syndrome (MDS)/myeloproliferative syndrome (MPS)

Solid Tumor\r\n* Failed or ineligible to receive autologous transplant or if autologous transplant would not offer > 20% chance of cure\r\n* Neuroblastoma\r\n** High risk with relapsed or refractory disease\r\n* Soft tissue sarcoma (rhabdomyosarcoma, Ewing sarcoma, primitive neuroectodermal tumor, or other high-risk extracranial solid tumors)\r\n** Relapsed or primary refractory metastatic\r\n** 1st complete remission, but very high-risk features (i.e., < 20% survival with conventional therapy)\r\n* Osteosarcoma\r\n** Failure to achieve complete remission (CR) following initial therapy\r\n** Relapsed with pulmonary or bone metastases and did not achieve a CR with surgery and/or chemotherapy

Patients must be in a >= 2nd complete remission as indicated by appropriate radiologic evaluations at the time of study entry

Patients with OS in first complete remission

Creatinine (Cr) < 2.0

Patients with B-lineage acute lymphocytic leukemia (ALL) in hematologic complete remission (CR) with molecular failure (ie, had never achieved an MRD-negativity status before blinatumomab) or had a molecular relapse (ie, became MRD positive after having been MRD negative) starting at any time point after 3 months of frontline therapy; molecular disease or minimal residual disease is defined by a value of at least of 1 x 10^-4 by multicolor flow cytometry

Patients with Philadelphia chromosome positive (Ph+) ALL can be enrolled in CR1 or CR2 and beyond; a tyrosine kinase inhibitor (TKI) will be added at the discretion of the treating physician; MRD for these patients will be defined by PCR of 0.1% and above (International Scale).

Patients likely to have a significantly better durable response to allogeneic transplant alone (better than 60% progression free longer than 2 years) includes: those with myeloproliferative diseases or hemoglobinopathies with over 50% T cell subset engraftment (assessed around 100 days post transplant); it is not anticipated that any such patients would be transplanted within our program, however but those in first remission acute myeloid leukemia (AML) patients with good risk standard genetics or normal genetics with either nucleophosmin (NPM)1 or CCAAT/enhancer binding protein alpha (CEBPA) mutations, first chronic phase chronic myelogenous leukemia (CML) without kinase gene mutations, follicular lymphoma patients in first remission who only required 1 regimen to attain remission all would be excluded from this protocol

Eligible patients will have a histopathologically confirmed diagnosis of hematologic malignancy in one of the following categories: \r\n* Acute myelogenous leukemia \r\n** In first complete remission (CR1) with poor risk cytogenetics according to National Comprehensive Cancer Network (NCCN) guidelines for acute myeloid leukemia (AML): monosomal karyotype, -5, 5q-,-7,7q-,11q23-non t(9;11), inv (3), t(3;3), t(6;9), t(9;22) and complex karyotypes (>= 3 unrelated abnormalities [abn]) and normal cytogenetics with fms-related tyrosine kinase 3 (FLT3)-internal tandem duplications (ITD) mutation \r\n** In second complete remission (CR2) or third complete remission (CR3) \r\n** With chemosensitive primary refractory disease \r\n* Acute lymphocytic leukemia \r\n** In CR1 with poor risk cytogenetics: \r\n*** For adults according to NCCN guidelines for acute lymphoblastic leukemia (ALL): hypoploidy (< 44 chromosomes); t(v;11q23): mixed lineage leukemia (MLL) rearranged; t(9;22) (q34;q11.2); complex cytogenetics (5 or more chromosomal abnormalities); high white blood cell (WBC) at diagnosis (>= 30,000 for B lineage or >= 50,000 for T lineage) \r\n*** For pediatrics t(9;22), intrachromosomal amplification of chromosome 21 (iAMP21)loss of 13q, and abnormal 17p \r\n** In CR2 or CR3 \r\n** With chemosensitive primary refractory disease \r\n* Myelodysplastic syndrome in high-intermediate (int-2) and high risk categories

Patients must meet one of the following criteria:\r\n* The presence of refractory or progressive disease (PD) prior to or following completion of standard therapy for MIBG avid tumors\r\n* For patients with neuroblastoma, the presence of mixed response (MR), or no response (NR) following the completion of A3973 or equivalent induction therapy, or the presence of a partial response (PR) with high Curie score (> 2) following induction therapy \r\n* Patients with de novo high risk neuroblastoma who have completed standard induction therapy and do not achieve a complete response (CR), very good partial response (VGPR), or PR with low Curie score post induction are eligible; for patients with neuroblastoma the revised International Neuroblastoma Response Criteria (INRC) shall be used to assess pre-treatment disease status

Burkitt or lymphoblastic lymphomas\r\n* High-risk disease in remission\r\n* Progression after >= 1 previous regimen\r\n* Non-CR after salvage regimen

Acute myelogenous leukemia\r\n* In first complete remission (CR1) in addition to one of the criteria outlined\r\n* Second or greater complete remission\r\n* Secondary acute myeloid leukemia (AML) from antecedent myeloid neoplasm, myelodysplasia, or previous chemotherapy (chemo) or radiotherapy

Acute lymphocytic leukemia\r\n* In complete first remission (CR1) in addition to one of the criteria outlined\r\n* Second or greater complete remission

Natural killer (NK) cell neoplasms\r\n* First complete remission (CR) for patients with high risk natural killer cell neoplasms including myeloid/NK cell precursor acute leukemia, blastic NK-cell lymphoma, aggressive NK-cell leukemia and nasal-type extranodal NK-cell lymphoma in first complete remission\r\n* Second or greater CR

Recipients with AML in CR1 must have one of the following:\r\n* Adverse cytogenetics (as evaluated by history) as defined as complex karyotype (> 3 abnormalities); inv(3) or t(3;3); t(6;9); t(6;11); monosomy 7; trisomy 8, alone or with an abnormality other than t(8;21), t(9;11), inv(16) or t(16;16); or t(11;19)(q23;p13.1)\r\n* Cytogenetically normal AML (CN-AML) with mutations in FMS-like tyrosine kinase 3 (FLT3), deoxyribonucleic acid (DNA) methyl transferase 3A (DMNT3A), or additional sex coombs like 1 (ASXL1)\r\n* Primary induction failure, defined as failure to achieve CR with primary induction chemotherapy\r\n* Secondary AML, defined as AML related to antecedent myeloid neoplasm or cytotoxic chemotherapy\r\n* Hyperleukocytosis, white blood cell (WBC) > 100,000, at diagnosis

Recipients with acute lymphoblastic leukemia (ALL) in CR1 must have one of the following:\r\n* Adverse cytogenetics defined as translocations involving t(4;11), t(1;19), t(8;14), 11q23, t(9;22) or bcr-abl rearrangement or complex cytogenetic abnormalities\r\n* Presence of minimal residual disease using multicolor flow cytometry or other analytic technique after primary induction chemotherapy\r\n* Primary induction failure, defined as failure to achieve CR with primary induction chemotherapy

Patients with a pathologically confirmed diagnosis of systemic mature T-cell non-Hodgkin lymphoma (NHL) with City of Hope pathology review as per World Health Organization (WHO) classification of lymphomas 2008, who are deemed eligible for high dose therapy and AHCT including patients in:\r\n* T-NHL histologies including peripheral T-cell lymphomas (PTCLs), cutaneous T-cell lymphomas (CTCLs) and natural killer (NK)/T cell lymphomas\r\n** First remission after initial first-line therapy (CR1) in PTCL patients, except for anaplastic lymphoma receptor tyrosine kinase (ALK)+ anaplastic large cell lymphoma (ALCL) and CTCL; patients with minimal residual disease after induction therapy may also be eligible at the discretion of the principal investigator (PI)\r\n** Relapsed/refractory disease, stable disease, partial remission (PR) or complete remission (CR), who have received at least 2 lines of therapy, and do not have an adequate allogenetic stem cell transplant option

Prior treatment (one of the following scenarios):\r\n* Primary refractory: for newly diagnosed AML, patients must have achieved two consecutive induction attempts without achieving complete remission\r\n* Relapsed/refractory: for patients initially in complete remission whose AML relapses > 6 months after preceding remission, one re-induction must be attempted to be eligible\r\n* Relapsed/untreated: for AML patients with early relapse, in whom the preceding remission is shorter than 6 months duration, no re-induction regimen is necessary to be eligible

Patients with T cell acute lymphoblastic leukemia (ALL) must be in complete remission and minimal residual disease (MRD) negative (-) by flow cytometry and molecular studies

Patients with neoplastic hematological disorders with indication of allogeneic transplant according to the National Comprehensive Cancer Network (NCCN) or other standard guidelines as follows:\r\n* Acute lymphoblastic leukemia (ALL) with high-risk features or relapsed disease.\r\n* Hodgkin or non-Hodgkin lymphoma (HL or NHL): relapsed disease where remission duration is less than 1 year, relapse after previous autologous transplant, or failure to achieve complete remission (CR) with chemotherapy\r\n* Myeloid malignancy (acute myeloid leukemia [AML] with intermediate/high-risk features [per NCCN criteria] or relapsed disease, OR chronic myeloid leukemia [CML] in hematological remission or chronic phase)

Acute myelogenous leukemia (AML): high-risk AML including:\r\n* Antecedent hematological disease (e.g., myelodysplasia [MDS])\r\n* Treatment-related leukemia\r\n* Complete remission (first complete remission [CR1]) with poor-risk cytogenetics or molecular markers (e.g. fms-related tyrosine kinase 3 [Flt 3] mutation, 11q23, del 5, del 7, complex cytogenetics)\r\n* Second complete remission (CR2) or third complete remission (CR3) or induction failure or 1st relapse with either\r\n** =< 10% blasts in the marrow or \r\n** =< 5% blasts in the peripheral blood

Acute lymphoblastic leukemia (ALL)\r\n* High-risk CR1 including:\r\n* Poor-risk cytogenetics (e.g., Philadelphia chromosome t(9;22) or 11q23 rearrangements)\r\n* Presence of minimal disease by flow cytometry after 2 or more cycles of chemotherapy\r\n* No complete remission (CR) within 4 weeks of initial treatment\r\n* Induction failure\r\n* CR2 or CR3 with either\r\n** =< 10% blasts in the marrow or \r\n** =< 5% blasts in the peripheral blood

Subjects must meet one of the disease classifications listed below:\r\n* Acute leukemias (includes T lymphoblastic lymphoma); remission is defined as < 5% blasts with no morphological characteristics of acute leukemia (e.g., Auer Rods) in a bone marrow with > 20% cellularity, peripheral blood counts showing absolute neutrophil count (ANC) > 1000/ul, including patients in complete remission with incomplete platelet recovery (CRp)  \r\n** Acute lymphoblastic leukemia in high risk first complete remission (CR1) as defined by at least one of the following: \r\n*** Adverse cytogenetics such as t(9;22), t(1;19), t(4;11), mixed lineage leukemia (MLL) rearrangements \r\n*** White blood cell counts > 30,000/mcL\r\n*** Patients over 30 years of age\r\n*** Time to complete remission > 4 weeks\r\n*** Presence of extramedullary disease\r\n** Acute myelogenous leukemia in high risk CR1 as defined by at least one of the following: \r\n*** Greater than 1 cycle of induction therapy required to achieve remission \r\n*** Preceding myelodysplastic syndrome (MDS) \r\n*** Presence of Fms-like tyrosine kinase 3 (Flt3) abnormalities\r\n*** French-American-British classification (FAB) M6 or M7 leukemia or\r\n*** Adverse cytogenetics for overall survival such as:\r\n**** Those associated with MDS \r\n**** Complex karyotype (>= 3 abnormalities)\r\n**** Any of the following: inv(3) or t(3;3), t(6;9), t(6;11), + 8 [alone or with other abnormalities except for t(8;21), t(9;11), inv(16) or t(16;16)], t(11;19)(q23;p13.1)\r\n** Acute leukemias in 2nd or subsequent remission\r\n** Biphenotypic/undifferentiated leukemias in 1st or subsequent complete remission (CR)\r\n** High-risk MDS status-post cytotoxic chemotherapy\r\n** Myelofibrosis\r\n* Burkitt’s lymphoma: second or subsequent CR\r\n* Lymphoma\r\n** Chemotherapy-sensitive (complete or partial response) large cell, mantle cell or Hodgkin’s lymphomas that have failed at least 1 prior regimen of multi-agent chemotherapy and are ineligible for an autologous transplant or relapsed/progressed after autologous stem cell transplant\r\n** Marginal zone B-cell lymphoma or follicular lymphoma that has progressed after at least two prior therapies (excluding single agent Rituxan) and are ineligible for an autologous transplant or relapsed/progressed after autologous stem cell transplant

ARM 1 - AML: Research patients enrolled are those patients with relapsed or refractory CD123+ AML de novo, or secondary OR participant who are at high risk for disease recurrence\r\nNOTE: CD123+ biphenotypic acute leukemia or CD123+ acute lymphoblastic leukemia (ALL) may also be considered but only after discussion with the study principal investigator (PI)\r\n* Relapsed AML is defined as patients that had a first complete remission (CR) before developing recurrent disease (increased bone marrow blasts)\r\n* Refractory AML is defined as patients that have not achieved a first CR after 2 cycles of induction chemotherapy; for patients with AML evolving from myelodysplastic syndrome, they should have completed at least one cycle of induction chemotherapy

MRD will be defined in this protocol by presence of malignant cells at 0.01% or more by flow cytometry or polymerase chain reaction (PCR) analysis at the completion of initial remission induction therapy

Patients who have undergone an autologous HCT for the treatment of DLBCL and are in a complete remission (CR), partial remission (PR) or have stable disease (SD) at the day 28 post-transplant reassessment

Patients aged 18 to 55 years with high risk AML who have achieved their FIRST complete remission (CR) or complete remission with incomplete recovery (CRi) within 12 months of enrollment and are not immediately candidates for allogeneic stem cell transplant; patients above age 55 who are not eligible for other protocols may be considered for enrollment on a case by case basis after discussion with the principal investigator (PI)

Patients in their FIRST CR or CRi may be eligible for enrollment only if they have a high risk feature, including, but not limited to: adverse karyotype, fms-related tyrosine kinase 3 (FLT3) mutation, history of antecedent hematologic disorder (AHD), presence of dysplasia in the bone marrow, therapy-related AML, history of requiring more than 1 cycle of intensive induction chemotherapy to achieve first remission, or presence of persistent minimal residual disease (detected by cytogenetics, molecular markers, or flow cytometry) at any point after initial induction cycle; patients aged >= 18 years with AML who have achieved a SECOND CR or CRi within 12 months of enrollment and are not immediately candidates for allogeneic stem cell transplant are also eligible

Creatinine measurement (Cr) < 1.7

Acute lymphocytic leukemia or acute myelogenous leukemia who are not in first remission or second remission i.e. after failing induction therapy, or in relapse or beyond second remission; (prior therapy with VP-16 and Cytoxan is allowed)

Relapsed or refractory B-cell acute lymphoblastic leukemia (ALL)\r\n* 1st or greater bone marrow (BM) relapse OR\r\n* Any marrow relapse after allogeneic hematopoietic stem cell transplant (HSCT) and > 100 days from transplant OR\r\n* For patients with refractory disease:\r\n** < 60 years old that have not achieved a CR after >= 2 or more chemotherapy regimens\r\n** >= 60 years old that have not achieved a CR after 1 prior chemotherapy regimen\r\n** Patients with Philadelphia chromosome positive (Ph+) ALL are eligible if they have failed tyrosine kinase inhibitor therapy

Patients in complete remission with no assessable disease

Patients with hematologic malignancies for whom autologous stem cell transplantation is deemed clinically appropriate:\r\n* Non-Hodgkin’s lymphoma, or Hodgkin’s lymphoma: either in a first complete remission (CR1) or refractory/relapsed with chemosensitive disease in a complete remission (CR) or partial remission (PR)\r\n* Multiple myeloma in first or second remission; patients with CR or PR will be eligible for this protocol

Disease Criteria: \r\n* ALL in complete remission (CR) at the time of transplant; remission is defined as “less than 5.0% bone marrow lymphoblasts by morphology,” as determined by a bone marrow aspirate obtained within 2 weeks of study registration\r\n* Philadelphia chromosome positive ALL is allowed\r\n* Lymphoid blastic crisis of chronic myelogenous leukemia (CML) will be included (provided that patients achieve CR)

Patients with one of the following diseases: acute myeloid leukemia (AML): a. first complete remission with high-risk features defined as: (i) greater than 1 cycle of induction therapy required to achieve remission; (ii) preceding myelodysplastic syndrome (MDS); (iii) presence of FLT3 mutations or internal tandem duplication or other mutations associated with poor-risk AML (e.g. DNMT3A, TET2); (iv) French-American-British Classification (FAB) M6 or M7 classification; (v) adverse cytogenetics: -5, deletion (del) 5q, -7, del7q, abnormalities involving 3q, 9q, 11q, 20q, 21q, 17, +8 or complex karyotype (> 3 abnormalities); (vi) treatment-related AML, or b. second or greater remission; patients beyond second remission have to be in complete remission (CR) at transplant to be eligible, or c. primary induction failure with partial response to therapy who achieve adequate cytoreduction

DIAGNOSIS REQUIREMENT FOR PHASE I PATIENTS: Refractory AML without complete remission (CR) after induction therapy (primary induction failure) or relapsed AML after obtaining a CR OR

PHASE II ONLY: More than one course of salvage chemotherapy for primary induction failure or AML relapsing after first complete remission (CR1)

For Phase II Only: Patients with MDS, CMML or AML who are either: Age 60 years or older and newly diagnosed, previously untreated. Prior therapy with hydroxyurea or single agent ara-C for the purpose of control of WBC is acceptable.; Age 18 years or older and with refractory or relapse disease who have received no more than one prior treatment regimen and will be receiving first salvage. For this purposes, a second induction cycle with the same drugs used during the first cycle, consolidation chemotherapy or stem cell transplant in CR (or CRp or CRi) will be considered part of the prior regimen. Prior therapy for MDS (or other malignancies) is not considered a prior regimen for AML in patients who progress from MDS (or other malignancies).;

Patients who had anything less than a CR (PR, SD or progressive disease) to their last salvage regimen

High risk hematologic malignancy\r\n* High risk acute lymphoblastic leukemia (ALL) in complete remission 1 (CR1); examples include, but not limited to: t(9;22), hypodiploid, minimal residual disease (MRD) > 1% at the end of induction, M2 or greater marrow at the end of induction, infants with mixed-lineage leukemia (MLL) fusion or t(4;11)\r\n* ALL in high risk complete remission 2 (CR2); examples include, but not limited to t(9;22), bone marrow (BM) relapse < 36 months CR1, T-ALL, very early (< 6 months CR1) isolated central nervous system (CNS) relapse\r\n* ALL in complete remission 3 (CR3) or subsequent\r\n* Acute myeloid leukemia (AML) in high risk CR1 (diagnosis of AML includes myeloid sarcoma); examples include but not limited to: preceding myelodysplastic syndrome (MDS), 5q-, -5, -7, French-American-British Cooperative group (FAB) M6, FAB M7 not t(1;22), MRD > or = 5% on day 22 (AML08), MRD > 0.1% after two cycles of induction, M3 marrow after once cycle of induction, M2 marrow after two cycles of induction, fms-related tyrosine kinase 3 (FLT3)-internal tandem duplication (ITD)\r\n* AML in CR2 or subsequent\r\n* AML in relapse with < 25% blasts in BM\r\n* Therapy related AML, with prior malignancy in CR > 12 months\r\n* MDS, primary or secondary\r\n* NK cell, biphenotypic, or undifferentiated leukemia in CR1 or subsequent\r\n* Chronic myeloid leukemia (CML) in accelerated phase, or in chronic phase with persistent molecular positivity or intolerance to tyrosine kinase inhibitor\r\n* Hodgkin lymphoma in CR2 or subsequent after failure of prior autologous HCT, or unable to mobilize stem cells for autologous HCT\r\n* Non-Hodgkin lymphoma in CR2 or subsequent after failure of prior autologous HCT, or unable to mobilize stem cells for autologous HCT\r\n* Juvenile myelomonocytic leukemia (JMML)\r\n* One of the following hematologic malignancies that are refractory (includes chemoresistant relapse or primary induction failure)\r\n** ALL\r\n** AML\r\n** CML (blast crisis)\r\n** Hodgkin or non-Hodgkin lymphoma

Patients must have a histologically and cytological confirmed acute myeloid leukemia, high risk AML defined as:\r\n* Age > 60, or\r\n* Presence of complex cytogenetic abnormalities (with > 3 cytogenetic abnormalities), del (7q, -5, -7), t(9,22), 11q (23) or high risk mutations by fluorescence in situ hybridization (FISH) eg mixed lineage leukemia (MLL) , FMS-like tyrosine kinase 3 positive (FLT-3 +), or\r\n* Secondary AML, or\r\n* A white blood cell count of > 50 x 10^9/L\r\n* Failure to achieve complete remission (CR) with single standard induction

Cohort B: newly diagnosed AML, failed to achieve complete remission (CR) with single standard induction chemotherapy (chemo)

PHASE I: Diagnosis of a hematological malignancy listed below (excluding myelofibrosis) in remission or with stable minimal residual disease\r\n* Acute myelogenous leukemia (AML) in 1st or subsequent remission or in relapse after any remission\r\n* Acute lymphoblastic leukemia (ALL) in 1st or subsequent remission or in relapse after any remission\r\n* Myelodysplastic syndrome either intermediate 1 or 2, or high risk by the International Prognostic Scoring System\r\n* Chronic myelogenous leukemia (CML) in accelerated or second chronic phase\r\n* Non-Hodgkin’s lymphoma (NHL) or Hodgkin’s disease (HD) in 2nd or greater complete remission, partial remission, or refractory relapse\r\n* Chronic lymphocytic leukemia (CLL), Rai stage 2-4, failing at least 2 prior regimens\r\n* Multiple myeloma (MM), stage 2-3\r\n* Myeloproliferative disorder or neoplasm

Initial diagnosis of poor -risk AML or MDS, treated with either stem cell transplant or cytarabine-based consolidation chemotherapy, within the past 60-185 days; the original diagnosis of AML or MDS must have been confirmed by bone marrow aspirate and/or biopsy review by a Johns Hopkins Hospital (JHH) hematopathologist; poor-risk AML is defined as disease that is therapy-related or arises from a previous marrow disorder, or de novo AML that is associated with any of the following characteristics: patient age 60 years or greater,\r\ntrilineage dysplasia, disease status greater than or equal to second complete remission (CR2), fms-related tyrosine kinase 3 (FLT3)/internal tandem duplication (ITD) mutations, detectable disease at time of consolidation chemotherapy or SCT, or poor-risk cytogenetics, which include abnormalities of chromosome 3, 5, or 7, trisomy 8, 11q23 abnormalities, t(6;9), 20q-, and complex karyotype

Secondary AML in 1st remission

AML in 1st relapse or >= 2nd remission

Acute lymphoblastic leukemia (ALL/LL) in 1st remission clinical or molecular features indicating a high risk for relapse; or ALL >= 2nd remission

Any patient, regardless of age or sex, with EBV-positive Hodgkin’s or non-Hodgkin’s lymphoma, (regardless of the histological subtype) or EBV (associated)-T/NK-lymphoproliferative disease or severe chronic active EBV (CAEBV); in second or subsequent relapse (or first relapse or with active disease if immunosuppressive chemotherapy contraindicated or multiply relapsed patients in remission who have a high risk of relapse) OR any patient with primary disease or in first remission if immunosuppressive chemotherapy is contraindicated, e.g. patients who develop Hodgkin disease after solid organ transplantation or if the lymphoma is a second malignancy e.g. a Richter’s transformation of chronic lymphocytic leukemia (CLL) (Group A); OR in remission or with minimal residual disease status after autologous or syngeneic stem cell transplantation (SCT) (Group B)

Any patient, regardless of age or sex, with EBV-positive Hodgkin’s or non-Hodgkin’s lymphoma (regardless of histologic subtype), or EBV (associated)-T/NK-lymphoproliferative disease or severe chronic active EBV (CAEBV) and; in second or subsequent relapse (or first relapse or with active disease if immunosuppressive chemotherapy contraindicated or multiply relapsed patients in remission who have a high risk of relapse) OR any patient with primary disease or in first remission if immunosuppressive chemotherapy is contraindicated, e.g. patients who develop Hodgkin disease after solid organ transplantation or if the lymphoma is a second malignancy e.g. a Richter’s transformation of CLL (Group A); patients with relapsed or refractory lymphoma that are eligible for a stem cell transplant will not be treated on this study as an alternative to transplant; OR in remission or with minimal residual disease status after autologous or syngeneic SCT (Group B)

Hodgkin lymphoma that is: \r\n* PIF (primary induction failure): did not enter complete remission with first line of therapy; Note: a patient with PIF who responds to salvage therapy with a PR or CR is also eligible (and would be considered PIF-sensitive)\r\n* Early 1st relapse: initial CR of > 3 months and < 12 months after 1st line chemotherapy\r\n* 1st relapsed HL in a patient who is not in CR after 2 cycles of salvage therapy\r\n* In 2nd or subsequent relapse (RL) whether in CR or not after salvage therapy

Creatinine (Cr) < 2.0

Patients with active AML or MDS at the time of the study (anything less than a complete remission) are not eligible for this protocol

Diagnosis of one of the following:\r\n* Previously untreated Ph-positive ALL (either t[9;22] and/or bcr-abl positive) (includes patients initiated on first course of hyper-CVAD before cytogenetics known)\r\n* Previously treated Ph-positive ALL, after 1-2 courses of chemotherapy with or without other tyrosine kinase inhibitors (TKIs)\r\n** If they achieved complete response (CR), they are assessable only for event-free and overall survival, or\r\n** If they failed to achieve CR, they are assessable for CR, event-free, and overall survival

Subjects with AML previously treated with initial induction therapy using a standard intensive chemotherapy regimen, including cytarabine and an anthracycline, and who are refractory to initial induction (primary refractory) or in relapse after such initial induction with or without prior HCT.

Be in first relapse (within 24 months of CR) or have primary refractory AML (refractory to initial induction therapy using 1 or 2 cycles of intensive anthracycline/cytarabine ± etoposide or cladribine induction) or have newly diagnosed high-risk AML as defined in this protocol.

CR or PR required; remission status will be assessed at the completion of induction chemotherapy and prior to enrollment on protocol

Patients treated on this study will have:\r\n* Acute leukemia in 1st or 2nd complete remission (CR)\r\n* MDS (myelodysplastic syndrome), specific subtypes of RA (refractory anemia) or RARS (refractory anemia with ringed sideroblasts) subtypes\r\n* Hodgkin or indolent non-Hodgkin’s lymphoma with chemosensitive disease\r\n* Myeloma without morphological evidence of disease, or a PR to the most recent therapy\r\n* Myeloproliferative disorders with at least a PR to current therapy\r\n* Aplastic anemia\r\n* A hematological or oncological disease (not listed) that meets the criteria reviewed above

Patients in first remission are eligible

Any patient with a hematologic or oncologic diagnosis in which allogeneic HSCT is thought to be beneficial, and in whom front-line therapy has already been applied; patients will be considered high-risk if they have any of the following:\r\n* Eastern Cooperative Oncology Group (ECOG) performance status of =< 2\r\n* Acute leukemia: requiring more than one chemotherapy regimen to obtain 1st complete remission (CR); second or greater CR, 1st relapse; any Philadelphia chromosome-positive (Ph+) acute lymphoblastic leukemia (ALL)\r\n* Chronic myelogenous leukemia (CML) 2nd chronic phase, accelerated phase, or blastic phase\r\n* Myelodysplastic syndromes (MDS) with International Prognostic Scoring System (IPSS) of intermediate 2 or greater\r\n* Any myeloproliferative disorder\r\n* Hodgkin lymphoma: relapsed, refractory, or primary induction failure\r\n* Non-Hodgkin lymphoma: relapsed, refractory, primary treatment failure, or not eligible for an autologous HSCT\r\n* Other conditions not listed will be assessed as high-risk by the principal investigator (PI)

AML in 1st remission - for patients whose AML does not have 'good risk' cytogenetic features (i.e. t 8;21, t15;17, inv 16)

Secondary AML in 1st remission

AML in 1st relapse or >= 2nd remission

Standard risk patients will include eligible patients, as defined above, who are receiving transplants as treatment for MDS in RA/RCMD, RARS, AML in 1st or 2nd remission, ALL in 1st CR, NH in 1st remission, MM in 1st remission, very good partial response, or 1st partial response on the CML in the first chronic phase or 1st remission

Acute lymphoblastic leukemia in high risk first complete remission (CR1) as defined by at least one of the following: \r\n* Adverse cytogenetics including but not limited to t(9;22), t(1;19), t(4;11), mixed lineage leukemia (MLL) rearrangements\r\n* White blood cell counts > 30,000/mcL\r\n* Patients over 30 years of age\r\n* Time to complete remission > 4 weeks\r\n* Presence of extramedullary disease\r\n* Minimal residual disease\r\n* Other risk factors determined by the patient’s attending physician to be high risk features requiring transplantation

Acute leukemias in second (2nd) or subsequent remission

Biphenotypic/undifferentiated leukemias in first (1st) or subsequent complete remission (CR)

Burkitt's lymphoma: second or subsequent CR

High-risk NB (as defined above) and in 1) first CR/VGPR at >= 6 months from initiation of immunotherapy using anti-GD2 antibody, or 2) second or subsequent remission; remission is defined as complete (CR) or very good partial (VGPR) remission, according to the International Neuroblastoma Response Criteria; urine catecholamine levels are no longer taken into consideration when staging; patients can be considered as in VGPR with 1 or 2 MIBG (+) sites that were previously-irradiated

High risk disease including at least one of the following:\r\n* Relapsed or refractory disease\r\n* Transformed lymphoma\r\n* Aggressive T-cell lymphoma\r\n* Failure to achieve completed remission (CR) following Auto SCT\r\n* Less than a 20% chance of event-free survival from autologous transplant determined by the treating physician and the Principal Investigator

Up to one cycle of prior induction therapy will be permitted to include patients in whom presence of \good-risk\ cytogenetics was initially missed; if the patient is in remission from induction therapy, he/she will receive post-remission therapy; if the patient is not in remission then he/she will receive induction therapy

Acute myelogenous leukemia (AML): \r\n* Complete first remission (CR1) at high risk for relapse such as: \r\n** Known prior diagnosis of myelodysplasia (MDS) or myeloproliferative disorder; \r\n** Therapy related AML; \r\n** White cell count at presentation > 100,000; \r\n** Presence of extramedullary leukemia at diagnosis; \r\n** Any unfavorable subtype by French-American-British (FAB) or World Health Organization (WHO) classification; \r\n** High-risk cytogenetics (e.g. those associated with MDS, abnormalities of 5, 7, 8, Philadelphia chromosome, complex karyotype) or high risk molecular abnormalities;\r\n** Requirement for 2 or more inductions to achieve CR1\r\n** Any patient with newly diagnosed AML with intermediate risk cytogenetics\r\n** Any patient unable to tolerate consolidation chemotherapy as would have been deemed appropriate by the treating physician\r\n* Complete second remission (CR2)

Acute lymphoblastic leukemia (ALL): \r\n* Complete first remission (CR1) at high risk for relapse such as: \r\n** White cell count at presentation > 30,000 for B-cell lineage and >100,000 for T-cell lineage; \r\n** Presence of a high-risk cytogenetic abnormality such as t(9;22), t(1;19), t(4;11) or other MLL rearrangements (11q23) or other high-risk molecular abnormality; \r\n** Failure to achieve complete remission after four weeks of induction therapy; \r\n** Any patient with newly diagnosed ALL >= 50 years-old;\r\n** Any patient unable to tolerate consolidation and/or maintenance chemotherapy as would have been deemed appropriate by the treating physician\r\n* Complete second remission (CR2)

Other acute leukemias that are ambiguous lineage or of other types e.g. blastic plasmacytoid dendritic cell neoplasm in CR1 or CR2

Any non-Hodgkins lymphoma (including chronic lymphocytic leukemia) or Hodgkin’s lymphoma at high-risk of relapse\r\n* Eligible patients with diffuse large cell (DLC) non-Hodgkin lymphoma (NHL) will:\r\n** Have relapsed disease following initial therapy but failed to mobilize or had bone marrow involvement and therefore are not suitable for an autologous transplant OR \r\n** Have failed an autologous transplant and be in CR after salvage chemotherapy\r\n* Eligible patients with transformed indolent NHL/CLL will: \r\n** Have complete response/partial response (CR/PR) of the large cell component of their disease after either salvage chemotherapy or an autologous transplant\r\n* Eligible patients with mantle cell NHL will: \r\n** Be high-risk as such as tumor protein 53 (p53) positivity and be in 1st CR/PR after initial therapy OR \r\n** Have relapsed disease following initial therapy and be in 2nd or 3rd CR/PR after salvage chemotherapy\r\n* Eligible patients with indolent B cell NHL (such as, but not limited to, follicular, small cell or marginal zone NHL) or CLL will have 2nd or subsequent progression (pre-allograft cytoreduction necessary but CR/PR not required)\r\n* Eligible patients with HL will be without progression of disease (POD) after salvage chemotherapy

Acute leukemia in morphologic relapse or with morphologic persistent disease (cytogenetic or molecular persistence/relapse in morphologic CR are eligible); MDS or CML or other myeloproliferative disorder with > 5% blasts; aggressive lymphoma or HL with POD after salvage chemotherapy

Acute myelogenous leukemia (AML) at the following stages:\r\n* High risk first complete remission (CR1), defined as:\r\n** Having preceding myelodysplasia (MDS)\r\n** High risk cytogenetics (high-risk cytogenetics: del (5q) –5, -7, abn (3q), t (6;9) complex karyotype (>= 5 abnormalities) with any minimal residual disease (MRD) status\r\n** Requiring >= 2 cycles chemotherapy to obtain complete response (CR)\r\n** High allelic ratio fms-related tyrosine kinase 3 (FLT3)/internal tandem duplications positive (ITD+)\r\n** Standard risk cytogenetics with positive MRD at end of induction \r\n* Second or greater CR\r\n* First relapse with < 25% blasts in bone marrow

Acute lymphocytic leukemia (ALL) at the following stages:\r\n* High risk first remission, as determined by treating physician as per current guidelines\r\n* Secondary remission, defined as:\r\n** Bone marrow relapse < 36 months from induction; or,\r\n** T-lineage relapse at any time; or,\r\n** Isolated CNS relapse or,\r\n** Slow reinduction (M2-3 at day 28) after relapse at any time\r\n* Any third of subsequent complete remission (CR)

Biphenotypic or undifferentiated leukemia in any CR or if in first (1st) relapse must have < 25% blasts in BM

Acute myelogenous leukemia (AML)\r\n* High risk first complete remission (CR1), as determined by treating physician as per current guidelines\r\n* Second or greater CR\r\n* First relapse with < 25% blasts in bone marrow\r\n* Patients with therapy-related AML whose prior malignancy has been in remission for at least 12 months

Chronic lymphocytic leukemia (must have all three): Rai Stage III/IV; progression after previous complete remission (CR) or partial remission (PR) including purine antagonist (i.e. fludarabine); recent chemotherapy responsiveness

Advanced non-Hodgkin lymphoma (NHL): A) low-grade NHL (Working Formulation A, B, C) following progression after initial therapy if asymptomatic at diagnosis (>= CR2, >= PR2; response duration < 1 year from last therapy) or if no CR was achieved (> PR1); at least one prior therapy of intermediate intensity (e.g. cyclophosphamide, doxorubicin, vincristine, prednisone [CHOP]); B) mantle zone lymphoma after any progression following initial therapy (> CR1, > PR1); at least one prior therapy of intermediate intensity (e.g. CHOP); C) intermediate grade lymphoma (> PR2); response duration < 1 year from prior therapy; D) high-grade NHL (IWF H, I, J) after initial therapy if >= stage III at diagnosis; after any progression even if localized (stage I, II) at diagnosis with prior response duration < 1 year; E) recent chemotherapy responsiveness after treatment with >= 3 intermediate intensity regimens

Advanced Hodgkin's disease beyond PR2 (>= CR3, >= PR3): recent chemotherapy responsiveness

Previously untreated T cell ALL including T cell lymphoblastic lymphoma; failure to one induction course of chemotherapy are eligible; patients in CR after =< 2 courses are also eligible

Poor Prognosis Non-Seminomas Germ Cell Tumor in >= partial response (PR)1/complete response (CR)1 or Good or Intermediate Prognosis Seminomas and Non-Seminomas Germ Cell Tumor in >= PR1 or >= CR2 as defined by the International Germ Cell Cancer Consensus Classification; Patients with increasing tumor markers only (i.e., no imaging evidence of progressive disease) are eligible for transplant

Acute myeloid leukemia: high risk first complete remission (CR)1 as evidenced by: \r\n* High risk cytogenetics; t(4;11) or other mixed lineage leukemia (MLL) rearrangements; chromosome 5, 7, or 19 abnormalities; complex karyotype (> 5 distinct changes)\r\n* >= 2 cycles to obtain complete remission (CR)\r\n*Second CR (CR2) or higher preceding myelodysplasia (MDS)\r\n* All patients must be in CR or early relapse (i.e., < 15% blasts in bone marrow [BM])

Acute lymphocytic leukemia: high risk CR1 as evidenced by: \r\n* High-risk cytogenetics: t(4;11) or other MLL rearrangements; hypodiploid; t(9;22)\r\n* > 1 cycle to obtain CR\r\n* CR2 or higher\r\n* All patients must be in CR as defined by hematological recovery, AND < 5% blasts by light microscopy within the bone marrow with a cellularity of >= 15%

Achieves PR or CR in response to B-RAF treatment (Cohort C)

Acute myeloid leukemia (AML): high risk complete response (CR)1 (as evidenced by preceding myelodysplastic syndromes [MDS], high risk cytogenetics, >= 2 cycles to obtain CR, erythroblastic or megakaryocytic leukemia; CR2+; all patients must be in CR as defined by hematological recovery, AND < 5% blasts by light microscopy within the bone marrow with a cellularity of >=15%

Acute lymphocytic leukemia (ALL): high risk CR1 as defined by cytogentics (such as t(9;22), t (1:19), t(4;11), other mixed lineage leukemia (MLL) rearrangements, hypodiploidy, or IKZF1 abnormalities), deoxyribonucleic acid (DNA) index < 0.81, > 1 cycle to obtain CR or presence minimal residual disease (MRD); patients in CR2+ are eligible; all patients must be in CR as defined by hematological recovery, AND < 5% blasts by light microscopy within the bone marrow with a cellularity of >= 15%

Very high risk pediatric patients with ALL; patients < 21 years are also considered high risk CR1 if they had M2 or M3 marrow at day 42 from the initiation of induction or M3 marrow at the end of induction; they are eligible once they achieved a complete remission

Large cell non-Hodgkin's lymphoma (NHL) > CR2/ > PR2; patients in CR2/PR2 with initial short remission (< 6 months) are eligible

Acute myeloid leukemia: high risk first complete remission (CR1) (as evidenced by preceding myelodysplastic syndrome [MDS], high risk cytogenetics such as those associated with MDS or complex karyotype, > 2 cycles to obtain complete response [CR] or erythroblastic and megakaryocytic); second or greater CR

Acute lymphoblastic leukemia/lymphoma: high risk CR1 as evidenced by high risk cytogenetics (e.g. t(9;22), t(1;19),t(4;11), other mixed-lineage leukemia (MLL) rearrangements, hypodiploidy or IKAROS family zinc finger 1 [IKZF1]), > 1 cycle to obtain CR or evidence of minimal residual disease (MRD); patients in second or greater CR are also eligible

Burkitts lymphoma in CR2 or subsequent CR

Have achieved a response (partial response (PR) or better) to at least 1 prior therapy.

Patients with relapsed or refractory AML. Relapsed AML is defined as relapse after achieving a response to initial therapy and refractory AML is defined as failure to achieve a response after one previous line of therapy. Response is defined as per IWG criteria (CR, CRi or CRp). Patients who are not candidates to receive or who decline standard of care therapy are also eligible.

Acute myeloid leukemia (AML) and related precursor neoplasms: 2nd or greater complete remission (CR); first complete remission (CR1) in patients > 60 years old; CR1 in =< 60 years old that is NOT considered as favorable-risk; favorable risk AML is defined as having one of the following:\r\n* t(8,21) without cKIT mutation\r\n* inv(16) or t(16;16) without cKIT mutation\r\n* Normal karyotype with mutated NPM1 and wild type FLT-ITD\r\n* Normal karyotype with double mutated CEBPA\r\n* Acute prolymphocytic leukemia (APL) in first molecular remission at the end of consolidation

Acute lymphoblastic leukemia (ALL)/lymphoma: second or greater CR; CR1 unable to tolerate consolidation chemotherapy due to chemotherapy-related toxicities; CR1 high-risk ALL; high risk ALL is defined as having one of the following:\r\n* Evidence of high risk cytogenetics, e.g. t(9;22), t(1;19), t(4;11), other MLL rearrangements, IKZF1\r\n* 30 years of age or older at diagnosis\r\n* White blood cell counts of greater than 30,000/mcL (B-cell [B]-ALL) or greater than 100,000/mcL (T-cell [T]-ALL) at diagnosis\r\n* CNS leukemia involvement during the course of disease\r\n* Slow cytologic response (> 10% lymphoblasts in bone marrow on day 14 of induction therapy)\r\n* Evidence of persistent immunophenotypic or molecular minimal residual disease (MRD) at the end of induction and consolidation therapy

Very high risk pediatric patients with ALL: patients < 21 years are also considered high risk CR1 if they had M2 or M3 marrow at day 42 from the initiation of induction or M3 marrow at the end of induction; they are eligible once they achieve a complete remission

Diffuse large cell non-Hodgkin lymphoma (NHL) > CR/> PR: patients in CR/PR with initial short remission (< 6 months) are eligible, or those who have failed/or are not eligible for autologous transplant

Biphenotypic/undifferentiated/prolymphocytic leukemias in first or subsequent CR

>=6 months after completing any line of chemotherapy, or after autologous stem cell transplantation, and having attained either a very good partial response (VGPR) or a complete response (CR), and without the need for haematological maintenance therapies Inclusion Criteria for Group 3

Confirmed free light chain complete response (CR) during the first three cycles of first-line chemotherapy where at least the first cycle has been with cyclophosphamide, bortezomib, dexamethasone (CyBorD).

Patients with a history of any other cancer, unless in complete remission, and off all therapy for that disease for a minimum of 5 years

Acute lymphoblastic leukemia (ALL): induction failure, primary refractory to treatment (do not achieve complete remission after first course of therapy) or are beyond first remission including second or greater remission or active disease; patients in first remission are eligible if they are considered high risk, defined as any of the following detected at any time: with t(9;22) or t(4;11), hypodiploidy, complex karyotype, secondary leukemia developing after cytotoxic drug exposure, and/or evidence of minimal residual disease, or acute biphenotypic leukemia, or double hit non-Hodgkin's lymphoma

Hodgkin's disease (HD): induction failures, second or third complete remission, or relapse (including relapse post autologous hematopoietic stem cell transplant)

AML and ALL in 2nd or subsequent CR

Secondary AML in CR

Inclusion Criteria:\n\n        2.3.1 Inclusion Criteria for the Biology (KIR2DL1 Polymorphisms/ALL MRD), Comparative\n        Outcomes, and Cost Effectiveness Trial\n\n          1. Any patient with ALL, AML, or MDS who is deemed eligible for and undergoes HCT at\n             participating centers who provides consent for the KIR2DL1 polymorphisms, comparative\n             outcomes and cost-effectiveness portion of the trial.\n\n          2. Any ALL patient undergoing allogeneic HCT at participating centers is eligible for the\n             ALL deep sequence MRD portion of the trial.\n\n          3. Patients ineligible for the KIR-favorable haploidentical phase II trial who require\n             T-cell depletion may be treated using TCR ??+CD3+/CD19+ cell depletion. These patients\n             will be followed descriptively on this portion of the trial. Preparative regimen will\n             be at the discretion of the transplant center, but the options associated with this\n             protocol are recommended.\n\n        2.3.2 Inclusion Criteria for the KIR-favorable Haploidentical Phase II trial:\n\n          1. Age < 22 years\n\n          2. Disease and disease status:\n\n               -  ALL high-risk in first remission (<5% blasts by morphology pre-transplant)\n                  meeting criteria for transplant. Example CR1 indications: induction failure (>5%\n                  blasts by morphology on post-induction BM), minimal residual disease greater than\n                  or equal to 1% marrow blasts by morphology after induction, minimal residual\n                  disease by flow cytometry >0.01% after consolidation, hypodiploidy (<44\n                  chromosomes), persistent or recurrent cytogenetic or molecular evidence of\n                  disease during therapy requiring additional therapy after induction to achieve\n                  remission (e.g. persistent molecular BCR-ABL positivity).\n\n               -  ALL in second remission: B-cell; early (less than or equal to 36 months from\n                  initiation of therapy) BM relapse, late BM relapse with MRD >0.1% by flow\n                  cytometry after first induction therapy; T-cell or Ph+ with BM relapse at any\n                  time; very early (less than 18 months from initiation of therapy) isolated\n                  extramedullary relapse (T or B-cell)\n\n               -  Myelodysplastic syndrome (MDS): Any 2001 WHO classification subtype (Appendix I).\n                  RAEB-2 patients may proceed directly to transplant, but may also receive\n                  induction chemotherapy before transplant. Patients with ?20% morphologic marrow\n                  blasts will require induction therapy to reduce morphologic marrow blasts below\n                  5% before transplant.\n\n               -  High-risk AML defined as monosomy 5, del 5q, monosomy 7, M6, M7, t(6;9),\n                  FLT3-ITD, or patients who have greater than or equal to 25% blasts by morphology\n                  after induction, or who do not achieve CR after 2 courses of therapy. Also,\n                  patients with ? 0.1% MRD or evidence of progressive extramedullary disease after\n                  induction chemotherapy.\n\n               -  AML in second or subsequent morphologic remission.\n\n          3. Has not received a prior allogeneic hematopoietic stem cell transplant.\n\n          4. Does not have a suitable HLA-matched sibling donor available for stem cell donation.\n\n          5. Does not have a suitable matched or single antigen mismatched related or unrelated\n             donor available at any time (noted by search), or it is in the patient's best interest\n             as judged by the attending to move forward with stem cell transplantation rather than\n             wait for an unrelated donor to become available (refer to subsection 2.5.1 for further\n             details).\n\n          6. Has a suitable HLA KIR favorable haploidentical matched family member available for\n             stem cell donation.\n\n          7. Karnofsky Index or Lansky Play-Performance Scale ? 60 % on pre-transplant evaluation.\n             Karnofsky scores must be used for patients > 16 years of age and Lansky scores for\n             patients < 16 years of age.\n\n          8. Able to give informed consent if > 18 years, or with a legal guardian capable of\n             giving informed consent if < 18 years.\n\n          9. Adequate organ function (within 4 weeks of initiation of preparative regimen), defined\n             as:\n\n               -  Pulmonary: FEV1, FVC, and corrected DLCO must all be ? 50% of predicted by\n                  pulmonary function tests (PFTs). For children who are unable to perform for PFTs\n                  due to age, the criteria are: no evidence of dyspnea at rest and no need for\n                  supplemental oxygen.\n\n               -  Renal: Creatinine clearance or radioisotope GFR ³ 70 mL/min/1.73 m2 or a serum\n                  creatinine based on age/gender as follows:\n\n        Age Maximum Serum Creatinine (mg/dL) Male Female 1 to < 2 years 0.6 0.6 2 to < 6 years 0.8\n        0.8 6 to < 10 years 1 1 10 to < 13 years 1.2 1.2 13 to < 16 years 1.5 1.4\n\n        ? 16 years 1.7 1.4 The threshold creatinine values in this Table were derived from the\n        Schwartz formula for estimating GFR utilizing child length and stature data published by\n        the CDC.45\n\n          -  Cardiac: Shortening fraction of ? 27% by echocardiogram or radionuclide scan (MUGA) or\n             ejection fraction of ? 50% by echocardiogram or radionuclide scan (MUGA), choice of\n             test according to local standard of care.\n\n          -  Hepatic: \\SGOT (AST) or SGPT (ALT) < 5 x upper limit of normal (ULN) for age.\n             Conjugated bilirubin < 2.5 mg/dL, unless attributable to Gilbert's Syndrome.\n\n        Exclusion Criteria:\n\n          1. Pregnant or lactating females are ineligible as many of the medications used in this\n             protocol could be harmful to unborn children and infants.\n\n          2. Patients with HIV or uncontrolled fungal, bacterial or viral infections are excluded.\n             Patients with history of fungal disease during induction therapy may proceed if they\n             have a significant response to antifungal therapy with no or minimal evidence of\n             disease remaining by CT evaluation.\n\n          3. Patients with active CNS leukemia or any other active site of extramedullary disease\n             at the time of enrollment are not permitted. Note: Those with prior history of CNS or\n             extramedullary disease, but with no active disease at the time of pre-transplant\n             workup, are eligible.\n\n          4. Patients with genetic disorders (generally marrow failure syndromes) prone to\n             secondary AML/ALL with known poor outcome are not eligible (Fanconi Anemia, Kostmann\n             Syndrome, Dyskeratosis Congenita, etc).

History of lymphoma (Richter’s syndrome) unless in complete remission > 2 years without\r\nrelapse

COHORT 2: patients with high risk disease having undergone an allogeneic hematopoietic stem cell transplant from a 10/10 human leukocyte antigen (HLA) matched donor with one of the following disease subtypes:\r\n* Acute myeloid leukemia (AML) in CR1 with high risk features (European Leukemia Network [ELN]) at presentation\r\n** Diagnostic sample with either t(6;9), t(9;22), 11q23, inv 3, -5, -7, del17p, complex cytogenetics, NPMwt-flt3ITD+, OR p53 mutation (mut); patients whose samples have mutations in RUNX1 or ASXL1 are also eligible (unless the patient has favorable cytogenetics)\r\n* AML in CR1 with measurable minimal residual disease (MRD) by molecular (e.g., myeloid mutation profile, polymerase chain reaction [PCR] for NPM1, core-binding factor [CBF], mixed lineage leukemia [MLL]) or flow cytometry \r\n* AML not in CR1 (including patients with morphologic CR but with incomplete recovery, CRi)\r\n* Myelodysplastic syndrome (MDS) with complex cytogenetics, 17p deletion or p53 mutation, or JAK2 or RAS mutation\r\n* Treatment-related MDS or AML\r\n* Acute lymphoblastic leukemia (ALL) not in CR1\r\n* ALL with MRD\r\n* Any hematologic malignancy relapsed or with persistent disease after allogeneic hematopoietic stem cell transplant\r\n* Multiple myeloma\r\n* Non-Hodgkin lymphoma (NHL) with chemoresistant disease at time of transplant\r\n* Any patient undergoing allogeneic hematopoietic stem cell transplant and an anticipated rate of relapse > 80% based upon published data and for which there is consensus amongst the Hematologic Malignancies Tumor Study Group that enrollment is appropriate

In CR or complete remission with incomplete blood count recovery (CRi) after 1-2 induction chemotherapy documented by a bone marrow examination done within 2 weeks of starting cytarabine in this protocol

Must have achieved CR/CRi with less than 2 induction regimens that contain cytarabine and anthracycline

ESCLATION COHORT: Patients must have a diagnosis of newly diagnosed and/ or relapsed/refractory AML with any of the following:\r\n* Confirmed translocation involving 11q23\r\n* Partial tandem duplication(PTD) of the MLL gene (on 11q23)\r\n* FLT3-ITD (internal tandem duplication)\r\n* Increased Fgf2 in serum (2 standard deviations above control serum samples)\r\n* HOX(A9/A10) over-expression in bone marrow ( 2 standard deviations above control values in CD34+ cells from normal subjects)\r\n* Note: Relapsed or refractory AML is defined as either: \r\n** Recurrence of disease after a complete remission (CR), or \r\n** Failure to achieve CR with initial therapy

Meets one of the following disease criteria:\r\n* Primary (de novo) AML or higher-risk MDS with induction failure: No complete remission (CR) after 2 or more induction attempts with high dose chemotherapy or hypomethylating agents +/- other agents. Higher risk MDS defined as risk score > 4.5 based on the revised International Prognostic Scoring System (IPSS) criteria\r\n* Secondary AML (from antecedent hematologic malignancy or treatment-related): Not in CR after 1 or more cycles of chemotherapy\r\n* Relapsed AML: Blast count >= 5% in bone marrow or peripheral blood after prior attainment of CR; relapse at any time but >= 100 days following allogeneic hematopoietic cell transplantation (HCT)\r\n* Relapsed MDS: Morphologic evidence of relapse or increase in blasts >= 5% in bone marrow or peripheral blood after prior attainment of CR; relapse at any time but ?100 days following allogeneic HCT

High-risk acute myeloid leukemia (AML) with predicted risk of relapse higher than 30%, which includes, but not limited to the following:\r\n* Patients in morphological remission (complete response 1 [CR1] or beyond) with minimal residual disease as quantified either by flow cytometry, or by cytogenetics or molecular markers.\r\n* Patients with the following karyotypes in morphological complete remission (CR) or complete remission with incomplete hematologic recovery (CRi): European LeukemiaNet (ELN)-Intermediate I, Adverse, ELN-Intermediate-II. (Examples include monosomal karyotype, complex karyotype, mutant p53, mutant RUNX1, mutant ASXL1, mutant FLT3-ITD, mutant DNMT3A, inversion 3, T(6:9), KIT mutated core binding factor AML)

Treatment-related AML and secondary AML in morphological remission (CR1 or beyond) with minimal residual disease as quantified either by flow cytometry, or by cytogenetics or molecular markers

Patients with: A) diffuse large B-cell lymphoma (DLBCL) with one of the following: A.1) primary refractory (no CR to 1st line), A.2) high-risk relapse (CR1 < 6 months (mo), secondary International Prognostic Index [IPI] >1, high lactate dehydrogenase [LDH]), A.3) refractory relapse: no response to >= 1 salvage line and not eligible to receive other novel salvage therapies, such as chimeric antigen receptor T-cells (CAR-T) in a timely fashion or have already failed these; B) Hodgkin’s with one of the following: B.1) primary refractory (no CR or progressive disease [PD] within 3 months), B.2) high-risk relapse (CR1 < 1 year, extranodal relapse, B symptoms), B.3) refractory relapse: no response to >= 1 salvage line C) T-non Hodgkin's lymphoma (T-NHL) with one of the following: C.1) primary refractory (no CR to 1st line), C.2) high-risk relapse (within 6 months), C.3) refractory relapse to >= 1 line of salvage. D) any other lymphoma that is refractory or relapsed and that does not qualify for autologous transplant protocols of higher priority.

Relapsed and/or refractory AML from any duration of complete remission (CR); any number of prior therapies allowed

Subjects must be in primary remission

Cohort Inclusion Criteria - Group B: Subjects must have relapsed or refractory AML according to the WHO classification. For study purposes, refractory AML is defined as failure to ever achieve CR or recurrence of AML within 6 months of achieving CR; relapsed AML is defined as all others with disease after prior remission. (Group B is not currently recruiting. Expected to begin recruiting in 3rd quarter 2017.)

Any curable cancer with a complete response (CR) of > 2 years duration.

Chemistry: ALT/AST ? 3.0 x ULN, TBili ?1.5 x ULN, and Cr < 2 mg/dL

NOTE: All patients achieving CR or complete remission with incomplete blood count recovery (CRi) will receive consolidation when fit

Patients must have achieved a CR or CRi (or morphologic leukemia-free state for those patients proceeding to Arm G transplant)

Patients who have achieved a CR or CRi must have maintained peripheral blood evidence of a CR or CRi

Patients must have maintained peripheral blood evidence of a remission and must have a CR or CRi, confirmed on restaging bone marrow (BM) aspirate and biopsy and cytogenetic analysis

Patients must be > 28 days from the start of induction or re-induction chemotherapy, or from the start of consolidation cycle 1 (if received) and < 90 days following recovery from most recent treatment; and they must have achieved and maintained a response to induction therapy (CR, CRi, or “morphologic disease-free state”)

Relapsed after achieving remission with a prior therapy

Adult patients must have a hematological malignancy, as described below:\r\n* Acute leukemias:\r\n** Acute lymphoblastic leukemia (ALL) in first complete remission (CR1) that is NOT considered favorable-risk as defined by the presence of at least one of the following:\r\n*** Adverse cytogenetics such as t(9;22), t(1;19), t(4;11), other mixed lineage leukemia (MLL) rearrangements\r\n*** White blood cell counts of greater than 30,000/mcL (B-ALL) or greater than 100,000/mcL (T-ALL) at diagnosis,\r\n*** Recipient age older than 30 years at diagnosis,\r\n*** Time to CR greater than 4 weeks\r\n** Acute myelogeneous leukemia (AML) in first complete remission (CR1) that is NOT considered as favorable-risk; favorable risk is defined as having one of the following:\r\n*** t(8,21) without CKIT mutation\r\n*** inv(16) without CKIT mutation or t(16;16)\r\n*** Normal karyotype with mutated nucleophosmin (NPM1) and not FLT-IND\r\n*** Normal karyotype with double mutated CCAAT/enhancer binding protein alpha (CEBPA)\r\n*** Acute promyelocytic leukemia (APL) in first molecular remission at end of consolidation\r\n** Acute leukemias in second (2nd) or subsequent\r\n** Biphenotypic/undifferentiated/prolymphocytic leukemias in first or subsequent CR, adult T-cell leukemia/lymphoma in first or subsequent CR\r\n* Chronic myelogenous leukemia (CML) excluding refractory blast crisis; to be eligible in first chronic phase (CP1) patient must have failed or be intolerant to imatinib mesylate\r\n* Myelodysplastic syndrome (MDS): International Prognostic Scoring System (IPSS) intermediate (Int)-2 or high risk (i.e., refractory anemia with excess blasts [RAEB], RAEB in transformation [RAEBt]) or refractory anemia with severe pancytopenia or high risk cytogenetics; blasts must be < 10%\r\n* Chronic lymphocytic leukemia (CLL)/small lymphocytic lymphoma (SLL), marginal zone B-cell lymphoma or follicular lymphoma that have progressed after at least two prior therapies; patients with bulky disease (nodal mass greater than 5 cm) should be considered for debulking chemotherapy before transplant\r\n* Lymphoplasmacytic lymphoma, mantle-cell lymphoma, prolymphocytic leukemia are eligible after initial therapy in CR1+ or first or greater partial remission (PR1+)\r\n* Large cell non-Hodgkin lymphoma (NHL) > CR2/> PR2; patients in CR2/PR2 with initial short remission (< 6 months) are eligible\r\n* Lymphoblastic lymphoma, Burkitt lymphoma, and other high-grade NHL after initial therapy if stage III/IV in CR1/PR1 or after progression if stage I/II < 1 year\r\n* Multiple myeloma beyond PR2; patients with chromosome 13 abnormalities, first response lasting less than 6 months, or beta-2 microglobulin > 3 mg/L, may be considered for this protocol after initial therapy\r\n* Natural killer (NK) cell leukemia

Pediatric patients must have a hematological malignancy as described below:\r\n* AML: high risk CR1 (preceding MDS, intermediate to high risk cytogenetics, >= 2 cycles to obtain CR, French-American-British classification system [FAB] M6); CR2+, first relapse with < 25% blasts in bone marrow; morphologic complete remission with incomplete blood count recovery; therapy-related AML for which prior malignancy has been in remission for at least 12 months\r\n* ALL: high risk CR1 (Philadelphia chromosome positive [Ph+] ALL, MLL rearrangements with slow early response, hypodiploidy, end of induction M3 bone marrow, end of induction M2 with M2-3 at day 42, evidence of minimal residual disease [MRD]); high risk CR2 (Ph+ALL, bone marrow relapse < 36 months from induction, T-lineage relapse at any time, very early isolated central nervous system (CNS) relapse, slow induction after relapse at any time, evidence of MRD); >= CR3\r\n* NK cell lymphoblastic leukemia in any CR\r\n* Biphenotypic or undifferentiated leukemia in any CR or if in first relapse must have less than 25% blasts in bone marrow\r\n* Myelodysplastic syndrome (MDS) at any stage\r\n* Chronic myelogenous leukemia (CML) in chronic or accelerated phase\r\nEvidence of CNS leukemia must be treated and in CNS CR to be eligible for the study

Acute leukemia, primary refractory or beyond complete remission (CR)1, or minimal residual disease (MRD) positivity

Meets ONE of the following disease criteria:\r\n* Primary (de novo) AML induction failure: no CR after 2 or more induction attempts with high dose chemotherapy (note: hypomethylating agents such as azacitidine will count as induction failure)\r\n* Relapsed AML or secondary AML (from myelodysplastic syndrome [MDS] or treatment related): not in CR after 1 or more cycles of standard re-induction therapy\r\n** For patients > 60 years of age the 1 cycle of standard chemotherapy is not required if either of the following criteria is met:\r\n*** Relapse within 6 months of last chemotherapy\r\n*** Bone marrow (BM) blast count < 30% within 10 days of starting protocol therapy\r\n* AML relapsed > 4 months after transplant: no re-induction required, and no more than 1 re-induction cycle is allowed\r\n* Use of hydroxyurea is permitted to control blasts counts\r\n* Patients with prior central nervous system (CNS) involvement are eligible provided that it has been treated and cerebrospinal fluid (CSF) is clear for at least 2 weeks prior to enrollment; CNS therapy (chemotherapy or radiation) should continue as medically indicated during the study treatment

Subjects with a prior diagnosis of AML (excluding acute promyelocytic leukemia) based on World Health Organization classification who did not achieve complete response (CR) with their previous therapy or who have relapsed after achieving a complete response (CR) are eligible; any number of relapses will be eligible

Patients with MDS that has evolved to AML must be in remission

Patients with MDS evolved into AML that is not in remission

Diagnoses to be included:\r\n* Acute Myelogenous Leukemia at the following stages:\r\n** First remission (cytogenetic intermediate or high risk)\r\n** Second or subsequent remission\r\n*** Complete remission is defined as the absence of blasts in the peripheral circulation at the time of enrollment and < 5% blasts in the bone marrow\r\n* Chronic Myelogenous Leukemia at the following stages:\r\n** First or subsequent chronic phase:\r\n*** Patient refused tyrosine kinase therapy or is otherwise not suited for it\r\n*** Patient who has failed two lines of tyrosine kinase therapy (e.g., patient has not had a complete hematologic response and/or minor cytogenetic response by 3 months of second line therapy, major cytogenetic response by 12 months of second line treatment, or complete cytogenetic remission (CCyR) by 18 months of second line treatment)\r\n*** Patient who has lost complete hematologic response or major/complete cytogenetic response while on second line of therapy\r\n** Accelerated Phase – any one of the following symptoms:\r\n*** White blood cell (WBC) difficult to control (> 50 x 10^9/L despite therapy)\r\n*** Rapid doubling of WBC (< 5 days)\r\n*** 10% blasts in blood or marrow\r\n*** 20% blasts and/or promyelocytes in blood or marrow\r\n*** 20% basophils and/or eosinophils in blood\r\n*** Anemia or thrombocytopenia unresponsive to standard treatment\r\n*** Persistent thrombocytosis (> 1000 x10^9/L)\r\n*** Cytogenetic abnormalities in addition to Philadelphia positive (Ph+)\r\n*** Increasing splenomegaly\r\n*** Marrow fibrosis\r\n* Myelodysplastic syndromes at any of the following stages:\r\n** Refractory anemia\r\n** Refractory anemia with ringed sideroblasts\r\n** Refractory cytopenia with multilineage dysplasia\r\n** Refractory cytopenia with multilineage dysplasia and ringed sideroblasts\r\n** Refractory anemia with excess blasts-1 (5-10% blasts)\r\n** Refractory anemia with excess blasts-2 (10-20% blasts)\r\n** Myelodysplastic syndrome, unclassified\r\n** MDS associated with isolated del (5q) (only after failing lenalidomide)\r\n** Low risk MDS patients would be eligible only if transfusion-dependent and failing standard therapy (i.e. hypomethylating agents)\r\n** Chronic Myelomonocytic Leukemia\r\n* Primary Myelofibrosis\r\n** Intermediate-2 risk or high risk disease\r\n** Patients should have extinguished standard of care options prior to being considered for this trial\r\n* Chronic Lymphocytic Leukemia\r\n** Complete remission: the disease is completely absent and no relapse occurred prior to the preparative regimen; requires all of the following: \r\n** Nodular partial remission: complete response with persistent lymphoid nodules in bone marrow\r\n** Partial remission: reduction of more than 50% in the disease burden regardless of the number of lines of therapy received\r\n** Eligibility will be limited to those who have at least failed a fludarabine-based regimen\r\n* Mature B cell malignancies (including mantle cell lymphoma, follicular lymphoma, diffuse large B cell lymphoma, non-Hodgkin lymphoma not otherwise specified)\r\n** Patients should have extinguished standard of care options prior to being considered eligible for this trial\r\n** First complete remission (CR1) confirmed: complete disappearance of all known disease; the term “confirmed” is defined as a laboratory and/or pathological or radiographic determination\r\n** CR1 unconfirmed (CRU1): complete disappearance of all known disease with the exception of persistent scan abnormalities of unknown significance; the term “unconfirmed” is defined as scan abnormalities of unknown significance that are not biopsied or otherwise evaluated\r\n** Second complete remission positive (CR2+) confirmed: the recipient relapsed, then achieved complete absence of disease without radiographic evidence of disease\r\n** CR2+ unconfirmed: the recipient has achieved a second or subsequent complete response but has persistent radiographic abnormalities of unknown significance\r\n** Partial remission: reductions of >= 50% in greatest diameter of all sites of known disease and no new sites

Patients must have one of the following disease types:\r\n* Acute myeloid leukemia (AML) with any of the following:\r\n** In first complete remission (CR1) with high-risk features defined by any of the following:\r\n*** Presence of any of the cytogenetics abnormalities: -5/5q-, -7/7q-, t(9:22), t(6;9), inv(3), 9q, 11q23 abnormalities, or complex karyotype with 3 or more abnormalities per clone\r\n*** Need for 2 cycles of induction therapy to achieve CR1\r\n*** Preceding history of myelodysplasia or the prior administration of chemotherapy for a non-myeloid malignancy (i.e., secondary AML)\r\n** Patients in second or subsequent complete remission (CR2, CR3, etc.)\r\n** Primary refractory or relapsed AML with peripheral blood blasts < 2.0x10^9/l or with extramedullary disease (excluding active disease of the central nervous system)\r\n* Acute lymphoblastic leukemia (ALL) with any of the following:\r\n** In CR1 with high-risk features defined by any of the following cytogenetic abnormalities, including Ph+, t(4;11), 11q23 abnormalities, or t(1;9)\r\n** Patients in second or subsequent complete remission (CR2, CR3, etc.)\r\n** Primary refractory or relapsed ALL with peripheral blood blasts < 2.0x10^9/l or with extramedullary disease (excluding active disease of the central nervous system)\r\n* Myelodysplasia with any of the following features: \r\n** Refractory anemia with excess blasts with 11-20% blasts in the bone marrow (RAEB II)\r\n** Refractory anemia with excess blasts with 5-10% blasts (RAEB I) and poor risk cytogenetics (i.e., chromosome 7 abnormalities or complex karyotype with at least 3 abnormalities per clone)\r\n** Refractory cytopenia with multilineage dysplasia (RCMD) and poor risk cytogenetics (i.e., chromosome 7 abnormalities or complex karyotype with at least 3 abnormalities per clone)\r\n* Chronic myelogenous leukemia (CML) with one of the following criteria:\r\n** Accelerated phase, defined by any of the following:\r\n*** Blasts 10-19% of peripheral blood white cells or bone marrow cells\r\n*** Peripheral blood basophils at least 20%\r\n*** Persistent thrombocytopenia (< 100 x 10^9/l) unrelated to therapy, or persistent thrombocytosis (> 1000 x 10^9/l) unresponsive to therapy \r\n*** Increasing spleen size and increasing white blood cell (WBC) count unresponsive to therapy\r\n*** Cytogenetic evidence of clonal evolution (i.e., the appearance of an additional genetic abnormality that was not present in the initial specimen at the time of diagnosis of chronic phase)\r\n*** Resistance to tyrosine kinase inhibitors (e.g., imatinib, dasatinib, nilotinib) defined as no complete cytogenetic response even if the above criteria are not met\r\n** First chronic phase provided a complete hematologic remission was not achieved by 3 months or a complete cytogenetic remission by 18 months and the patient had received in addition to imatinib 400 mg daily at least one of the following options: a) imatinib 600-800 mg daily, b) nilotinib, or c) dasatinib\r\n** Second or subsequent chronic phase provided a complete hematologic remission was not achieved by 3 months or a major cytogenetic remission (< 35 % Philadelphia chromosome + metaphases) by 6 months and the patient had received in addition to imatinib 400 mg daily at least one of the following options: a) imatinib 600-800 mg daily, b) nilotinib, or c) dasatinib\r\n* Patients with aggressive non-Hodgkin’s lymphoma (NHL), including diffuse large cell lymphoma, mediastinal B-cell lymphoma, transformed lymphoma, mantle cell lymphoma, and peripheral T cell lymphoma, who also have one of the following criteria:\r\n** Failure to achieve complete remission to primary induction therapy\r\n** Relapsed and refractory to at least one line of salvage systemic therapy

Patients must have a histologically confirmed diagnosis of B-NHL, T-NHL, or HL; only patients with classical HL must have documented histologic demonstration of CD45+ cells adjacent to the Reed Sternberg cells; patients must have received at least one prior standard systemic therapy with documented recurrent or refractory disease; patients with mantle cell lymphoma (MCL), T-NHL, or other high-risk malignancies may be enrolled/transplanted in complete remission (CR)/first partial remission (PR1)

Hematologic malignancies diagnoses:\r\n* Acute lymphoblastic leukemia (ALL) with a history of bone marrow relapse in clinical remission (CR) #2 or greater, or in CR#1 if prior induction failure; or with an M1 marrow if unable to achieve CR\r\n* Philadelphia chromosome positive ALL patients who:\r\n** Have progressed through or relapsed following tyrosine kinase inhibitor (TKI) therapy or conventional myeloablative therapy OR\r\n** Are ineligible to receive tyrosine kinase inhibitor (TKI) therapy AND myeloablative hematopoietic stem cell transplant (HSCT)\r\n* Acute myelogenous leukemia (AML) with a history of bone marrow relapse in remission CR #2 or greater; or with an M1 marrow if unable to achieve CR; or in CR#1 if prior induction failure; or any of the following high-risk categories:\r\n** FMS-like tyrosine kinase 3/internal tandem duplication positive (FLT3/ITD+) with high allelic ratio > 0.4 (HR FLT3/ITD+) regardless of low risk features\r\n** Presence of monosomy 7, monosomy 5, or deletion (del)5q, without inversion (inv)(16)/t(16;16) or t(8;21) cytogenetics or nucleophosmin (NPM) or CCAAT enhancer-binding protein (CEBP) alpha mutations\r\n** AML without inv(16)/t(16;16), t(8;21), NPM, CEPB alpha mutations, monosomy 7, monosomy 5, del5q, or HR FLT3/ITD+, but with evidence of residual AML (>= 0.1%) at end of induction I\r\n* Hodgkin’s and non-Hodgkin’s lymphoma with refractory disease or relapse after at least one salvage regimen, or after autologous stem cell transplant\r\n* Juvenile myelomonocytic leukemia (JMML) with < 10% blasts in marrow and blood, who are not eligible for effective standard therapies\r\n* Chronic myelogenous leukemia (CML) with history of blast crisis (ALL/AML) or progressive disease failing tyrosine-kinase inhibitor (TKI)

Patients must be within 2 years of achieving CR following chemotherapy

Mantle cell lymphoma (MCL), T-NHL, or other high-risk malignancies may be enrolled/transplanted in complete remission (CR)/first partial remission (PR1)

Creatinine [Cr] < 2.0

NHL patients with resistant or refractory lymphoma (no partial remission [PR] following up to three cycles of combination chemotherapy) will be ineligible for transplant in this trial

Lymphoblastic lymphoma \r\n* All patients will be eligible in second or greater complete remission (CR) or first or subsequent partial remission (PR)\r\n* Patients with any high-risk features will be eligible in first complete remission \r\n* High risk features include: \r\n** Stage IV\r\n** Lactate dehydrogenase (LDH) > 2 x normal\r\n** >= 2 extranodal sites

Small lymphocytic lymphoma (SLL) or chronic lymphocytic leukemia (CLL)\r\n* Patients will be eligible in >= first complete remission (CR1) with molecularly negative disease\r\n* Patients in CR with molecularly positive disease or in PR will be excluded from autologous transplant

Follicular lymphoma\r\n* Patients will be eligible in >= first CR/PR (if treatment is delayed until clinically required)\r\n* Patients who are treated at diagnosis (without clinical symptoms necessitating treatment, such as B symptoms, bulky disease, marrow or other organ compromise) will be eligible in >= second CR/PR

Diffuse large B-cell lymphoma\r\n* All patients will be eligible in >= second complete remission (CR2) or >= first partial response (PR1)\r\n* Patients with a high intermediate or high International Protein Index (IPI) (>= 2 for age-adjusted IPI or >= 3 for IPI) at diagnosis will be eligible in first CR

Burkitt’s/Burkitt’s like\r\n* All patients except localized lymphoma will be eligible anytime after initial therapy (after achievement of first complete remission), or in partial remission if they fail to achieve CR\r\n* Patients with localized (stage I or Ziegler stage A) will be eligible only if they fail to achieve CR1 or after relapse

For stage I/II patients treated with primary radiation, they must have failed (no CR or progression after CR) at least one salvage combination chemotherapy treatment regimen

Chronic lymphocytic leukemia\r\n* Relapse post-fludarabine\r\n* Non-complete remission (CR) after salvage regimen

Special cases of high-risk lymphoma, including but not limited to: plasma dendritic cell type, hepato-splenic T cell type, gamma delta panniculitic T cell type, muco-cutaneous natural killer (NK) cell type, and stage III-IV nasal NK cell type\r\n* Primary treatment failure\r\n* Relapse after autologous SCT\r\n* Non-CR after salvage regimen\r\n*In first CR or any later CR

Acute myelogenous leukemia\r\n* CR #1 and “high-risk” (excludes t[8;21], t[15;17], or inv[16])\r\n* CR #2 or greater

Acute lymphocytic leukemia\r\n* CR #1 + “high-risk” (t[9;22] or bcr-abl+; t[4;11], 1[1;19], t[8;14])\r\n* In CR #2 or greater

Patients must have at least one of the following high-risk conditions listed below (criteria are consistent with existing criteria within Children's Oncology Group [COG] protocols):\r\n* Acute lymphocytic leukemia (ALL) in first complete remission (CR1) as defined by at least one of the following:\r\n** Hypodiploidy\r\n** Induction failure\r\n** Minimal residual disease (MRD) after consolidation\r\n* Acute myeloid leukemia (AML) in CR1 with high risk features defined as:\r\n** High allelic ratio fms-related tyrosine kinase 3 (FLT3)/internal tandem duplications (ITD) positive (+)\r\n** Monosomy 7\r\n** Del (5q)\r\n** Standard risk cytogenetics with positive minimal residual disease at the end of Induction I chemotherapy (for patients being treated on or according to COG AAML1031 who have had MRD studies sent to Seattle or performed at their local institution where the flow assay is sensitive enough to detect >= 0.1% blasts)\r\n* Acute leukemias in 2nd or subsequent complete remission (CR) (CR >= 2)\r\n* Mixed phenotype/undifferentiated leukemias in 1st or subsequent CR\r\n* Secondary or therapy related leukemias in CR >= 1\r\n* Natural killer (NK) cell leukemia or NK cell lymphoblastic leukemia/lymphoma CR >= 1\r\n* Myelodysplastic syndrome (MDS)\r\n* Juvenile myelomonocytic leukemia (JMML) (patients are eligible if they are not eligible for COG1221)\r\n* Prior transplant eligible if =< 18 years old (yo), >= 1 year has elapsed since BMT, and patient is off immunosuppression for >= 3 months with no GVHD; patients who have had a prior chemotherapy based preparative regimen are allowed to receive a TBI based prep, regardless of their disease\r\n* No known active central nervous system (CNS) involvement or extramedullary involvement by malignancy; such disease treated into remission is permitted\r\n* Remission is defined as morphology with < 5% blasts with no morphological characteristics of acute leukemia (e.g., Auer Rods) in a bone marrow with > 20% cellularity

Subject did not achieve complete remission/complete remission with incomplete hematologic recovery/complete remission with incomplete platelet recovery (CR/CRi/CRp) under initial therapy. A subject eligible for standard therapy must receive at least one cycle of an anthracycline containing induction block in standard dose for the selected induction regimen. A subject not eligible for standard therapy must have received at least one complete block of induction therapy seen as the optimum choice of therapy to induce remission for this subject.

Subject must have achieved a CR/CRi/CRp (criteria as defined by [Cheson et al, 2003], see Section 5.3) with first line treatment and has hematologic relapse.

Achieved a response of stable disease, partial response, or complete response following the last cycle of frontline treatment. In addition, patients must have relapsed less than or equal to 6 months from the completion of frontline therapy at the time of initial dosing in this clinical trial.

In first relapse (with duration of remission of 6 months or less) or refractory after prior therapy, with or without HSCT. Induction therapy must have included at least 1 cycle of an anthracycline/mitoxantrone-containing induction block at a standard dose.

Patients with life-threatening acute leukemia (high-risk ALL in 1st CR, ALL in 2nd CR, high-risk AML in 1st CR, AML in 2nd CR.) or myelodysplastic syndromes. Morphological CR must be documented and minimal residual disease measurement before transplantation is recommended.

Refractory as defined by not achieving a CR after 2 cycles of a standard chemotherapy regimen chemotherapy regimen or chemorefractory as defined by not achieving a CR after 1 cycle of standard chemotherapy for relapse leukemia OR

The previous induction regimen may have been a SCT with intent to induce a CR.

Consolidation and/or maintenance (including SCT) may have been given in CR/CRi, but are not counted as a line of treatment.

The previous induction regimen may have been a SCT with intent to induce a CR.

Consolidation and/or maintenance (including SCT) may have been given in CR/CRi, but are not counted as a line of treatment.

Primary refractory as defined by not achieving a CR after 2 cycles of a standard chemotherapy regimen or chemorefractory as defined by not achieving a CR after 1 cycle of standard chemotherapy for relapsed leukemia OR.

First Complete remission (CR)/ Complete remission with incomplete blood count recovery (CRi) with induction therapy + consolidation therapy within 4 months (+/- 7 days of achieving CR or CRi)

Have achieved CR/CRi following therapy with hypomethylating agents

Participants with hematologic malignancies or hematologic disorders for whom allogeneic stem cell transplantation is deemed clinically appropriate; eligible diseases and stages include:\r\n* Non-Hodgkin's lymphoma, or Hodgkin's lymphoma in second (2nd) or subsequent complete remission or in partial remission with documented chemosensitivity to the most recent chemotherapy regimen; prior autologous transplantation is required, unless deemed medically inappropriate by the treating physician\r\n* Multiple myeloma: relapsed but with chemosensitive disease; bone marrow plasma cells may not exceed 20% of the total cellularity\r\n* Chronic lymphocytic leukemia: any Rai stage III or IV, lymphocyte doubling time of 6 months, or stage I-II with progression after >= 2 chemotherapy regimens, in partial remission with documented chemosensitivity to the most recent chemotherapy regimen\r\n* Acute myelogenous or acute lymphoblastic leukemia in second or subsequent complete remission or in first remission with adverse cytogenetic/molecular features or a documented antecedent hematologic disorder\r\n* Myelodysplastic disorder\r\n* Myeloproliferative disorder including myelofibrosis, chronic myelogenous leukemia resistant to tyrosine kinase inhibitors\r\n* Aplastic anemia with no response to immunosuppressive therapy

History of a non-CLL malignancy except for adequately treated in situ, stage 1 or 2 carcinoma in Complete Response (CR), or any other cancer that has been in CR for >=2 years after end of cancer treatment.

Relapsed patients must have achieved a complete remission (CR) or CR with incomplete blood count recovery (CRi) lasting < 6 months with their last induction regimen

Patients must have achieved CR; patients who achieved only CRi or PR, and patients who relapse from CR before this registration are not eligible

Patients with a history of non-hematologic malignancies (except non-melanoma skin cancers) currently in a complete remission, who are less than 5 years from the time of complete remission, and have a > 20% risk of disease recurrence

Creatinine ? 1.5 x ULN or Cr Cl > 60 cc/min

Enrollment on protocol for collection of PBMC/T cells may occur for the following patients with CD19+ B-ALL\r\n* Patients whose disease meets one of the following 3 criteria:\r\n** Very high-risk (VHR)\r\n** Patients in first (1st) or subsequent marrow relapse (isolated or combined), at the time of relapse, during retrieval therapy, or after achievement of complete remission (CR)\r\n** Refractory disease\r\n** Definitions of VHR B-ALL include the following:\r\n*** National Cancer Institute (NCI) high risk (HR)-acute lymphoblastic leukemia (ALL) and age >= 13 years at diagnosis\r\n*** Overt central nervous system disease (CNS-3) leukemia at diagnosis\r\n*** Day 29/end of induction bone marrow (BM) minimal residual disease (MRD) > 0.01%\r\n*** Induction failure (M3 BM at day 29/end of induction)\r\n*** Hypodiploidy (n < 44 chromosomes and/or a deoxyribonucleic acid [DNA] index < 0.81)\r\n*** t(9;22) ALL (Philadelphia chromosome/Ph+ ALL) or Ph-like ALL\r\n*** t(17;19) ALL\r\n*** MLL gene rearrangement\r\n*** IKAROS family zinc finger 1 (Ikaros) (IKZF1) deletions\r\n*** Intrachromosomal amplification of chromosome 21 (iAMP21)\r\n* Please note patients that only meet the criteria for collection/storage of PBMCs will need to re-consented prior to infusion of genetically modified T-cells

Patients must be in morphologic complete response (CR), complete response with incomplete hematologic recovery (CRi), partial response (PR) by international working group criteria post induction therapy, or patients refractory to induction therapy provided they have < 1000 peripheral blasts/mm^3 and white blood cells (WBC) =< 10 x 10^9/L; patients in PR and/or those who are refractory and who have undergone only one course of induction therapy will be eligible only if one or more of the following criteria are met:\r\n* Patient preference to forgo further induction therapy in favor of low or intermediate-intensity therapy\r\n* Patients are deemed unlikely to benefit from anthracycline cytarabine induction therapies for any of the following reasons:\r\n** Therapy-related AML\r\n** Prior myelodysplastic syndrome or myeloproliferative neoplasm\r\n** The presence of cytogenetic or molecular genetic features place patient in the Intermediate-I, Intermediate-II or adverse genetic group as defined by the European LeukemiaNet\r\n* Patients who have experienced one or more Common Terminology Criteria for Adverse Events (CTCAE) version (v)4.0 grade 3-4 treatment related non-hematologic toxicity within 30 days of beginning the first course of induction therapy

AML French-American-British (FAB) M3 in first complete remission (CR1)

Received at least four treatments with MK-3475 beyond the date when the initial complete response (CR) was declared

Patients in complete remission with no evidence of evaluable disease by radiologic imaging

AML without complete remission (CR/CRc/CRi) after at least 2 induction therapies OR AML that has relapsed within 6 months after obtaining a CR OR AML that has relapsed more than 6 months after obtaining a CR, and has treatment failure (TF) or progressive disease (PD) following at least 1 re-induction regimen OR AML that has relapsed post-allogeneic transplantation

Any curable cancer with a complete response (CR) of > 5 years duration.

Patients must have a histologically confirmed diagnosis of B-NHL, T-NHL, or HL; only patients with classical HL must have documented histologic demonstration of CD45+ cells adjacent to the Reed Sternberg cells; patients must have received at least one prior standard systemic therapy with documented recurrent or refractory disease; patients with mantle cell lymphoma (MCL), T-NHL, or other high-risk malignancies may be enrolled/transplanted in complete remission (CR)/first partial remission (PR1)

Subjects treated with prior ipilimumab must have had partial response (PR), complete response (CR), or at least 6 months of stable disease followed by disease progression.

Patients eligible, at the time of starting treatment, for curative therapeutic approaches (such as allogeneic transplant) are not eligible for the trial; however, patients who achieve CR or partial response (PR) as a result of therapy on this trial may proceed to allogeneic transplant

Subjects with metastatic breast cancer who have achieved stable disease (SD), partial response (PR), or complete response (CR) after at least 1 regimen of anticancer therapy (i.e. chemotherapy or target therapy, either alone or in any combination). Involvement of supraclavicular lymph node is considered metastasis.

Concurrent systemic cancer therapy (hormones, biologics or chemotherapy) can be continued if distant metastases are non-responsive (i.e. no complete response [CR] or partial response [PR]) on that regimen for >= 8 weeks as assessed by the investigator

CR, partial response (PR) or stable disease (SD) after Step 1

Patients with multiple myeloma in complete remission (CR), partial remission (PR), or very good partial remission (VGPR), or symptomatic stable disease (no evidence of progression) including patients with light chain MM detected in the serum by free light chain assay

Patients with complete response (CR)/very good partial response (VGPR) disease

Histologically or cytologically confirmed extensive-stage disease small cell lung cancer (ED SCLC) with ongoing clinical benefit (stable disease [SD], partial response [PR], or complete response [CR]) following completion of 4 cycles of first-line platinum-based therapy

Chronic Lymphocytic Leukemia (CLL) in CR if RIC is to be used; in CR or partial response (PR) if FIC is to be used

Chemotherapy-sensitive lymphoma in status other than 1st CR

Have active, relapsed or refractory Acute Myeloid Leukemia (AML). Active, relapsed or refractory AML is defined as either (1) primary induction failure (PIF) after 2 or more cycles of chemotherapy, (2 first early relapse after a remission duration of fewer than 6 months, (3) relapse refractory to salvage combination chemotherapy containing high-dose AraC, and (4) second or subsequent relapse

For arms A and B, participants must have relapsed after or been refractory to first-line chemotherapy, i.e., they must have failed to achieve CR after first-line therapy or must have relapsed subsequently if they achieved CR; for arm C, participants will be eligible if transplant is performed as consolidation of first remission (partial or complete)

Participants must have chemosensitive disease prior to ASCT, defined as achieving at least a partial remission (as determined with PET imaging) to salvage treatment using International Harmonization Project (IHP) criteria; participants with cHL or DLBCL (arms A and B) transplanted in first (1st) remission after only one line of treatment are not eligible; participants with PTCL (arm C) transplanted beyond 1st remission are also not eligible

Patients meeting the Durie and Salmon criteria for initial diagnosis of multiple myeloma, requiring therapy and meeting one of the following:\r\n* After initial therapy in either first complete or partial remission or no objective response\r\n* After achieving initial response and later disease progression, patient will be eligible after subsequent therapy upon achievement of either complete or partial response

Patient is currently in complete cytogenetic remission (CCyR)

Patients will have relapsed at least once and returned to complete clinical remission after additional chemotherapy; interval surgery is permitted

Be actively receiving duvelisib monotherapy on the previous study (within 14 days of study entry) and demonstrating clinical benefit (complete response [CR]/ partial response [PR]/ stable disease [SD]) of continued use, or

Adults with pathologically confirmed acute myelogenous leukemia, in pathologically confirmed complete remission; patients with refractory anemia with excess blasts-2 (RAEB-2), who are in remission following therapy, can also be eligible

Documented response to ASCT (PR, VGPR, CR/stringent complete response [sCR]) according to IMWG criteria.

Creatinine (Cr) < 3

This treatment is for patients with high risk hematologic malignancies; high risk is defined as:\r\n* Any patient with a hematologic malignancy with residual disease after treatment with 1 or more chemotherapy regimens in whom achievement of remission with additional chemoradiotherapy is felt to be unlikely\r\n* Patients without morphologic evidence of disease but with high risk features which would predict for relapse despite remission at HSCT such as adverse cytogenetics, 3rd or greater complete remission (CR), or failure to recover peripheral blood counts to normal ranges; while these patients do not have detectable disease by current methods, like all patients they have non-detectable disease which in their case is highly aggressive

Early first relapse (< 36 months from original diagnosis) after achieving a CR (B-ALL) or first relapse any time following the original diagnosis after achieving a CR (T-ALL)

Relapse after achieving a CR following the first or subsequent relapse (i.e., ? 2 relapses) OR

Failing to achieve a CR from original diagnosis after at least 1 induction attempt

A very good partial response (VGPR) or better after induction therapy with/without consolidative high-dose therapy/autologous stem cell transplantation (HDT/ASCT).\r\n* Very good partial response (VGPR): \r\n** Serum and urine M-component detectable by immunofixation but not on electrophoresis or\r\n** >= 90% or greater reduction in serum M-component plus urine M-component < 100 mg per 24 hours (h)\r\n* Complete response (CR):\r\n** Negative immunofixation of serum and urine and\r\n** Disappearance of any soft tissue plasmacytomas and\r\n** < 5% plasma cells in bone marrow\r\n* Stringent complete response (sCR)\r\n** CR as defined above plus\r\n** Normal free light chain ratio and\r\n** Absence of clonal cells in bone marrow by immunohistochemistry or immunofluorescence\r\n* MRD positive by flow cytometry

receiving ibrutinib for at least 6 months with a response less than complete response/remission (CR) and have high-risk features as defined in inclusion criterion 5a

During dose escalation, patients must have received at least one prior therapy, need additional cytoreduction, and meet criteria for relapsed or refractory disease; relapsed disease is defined as a patient who previously achieved a CR or a PR, but after a period of six or more months demonstrates evidence of disease progression; refractory disease is defined as progression within six months of the last anti-leukemic therapy, or any response less than a CR or PR; patients who are previously untreated, and do not wish to receive chemotherapy or immunotherapy, are eligible for the dose expansion portion of the study

Subjects must have exhibited lack of CR or PR or progression within 6 months after the last dose of a chemotherapy induction regimen or RIT.

Acute myelogenous leukemia (AML) in complete morphological remission at study screening (Complete Remission with Incomplete Platelet Recovery (CRp) acceptable).

Acute lymphoblastic leukemia (ALL) in complete morphological remission at study screening (Complete Remission with Incomplete Platelet Recovery (CRp) acceptable).

Subjects must have entered the Maintenance Phase and are under ongoing maintenance treatment or subjects who stopped maintenance treatment because of a complete response (CR) or subjects with an initial partial response (PR) or CR or at least 3 months of stable disease (SD) on tumor assessment and who subsequently have a confirmed and documented disease progression (per immune-related Response Evaluation Criteria in Solid Tumors [RECIST] criteria)

Patients must demonstrate one of the following:\r\n* Relapse after first complete remission\r\n* Refractory to induction chemotherapy (for example, failure to respond to 1 or more cycles of daunorubicin and cytarabine) or to reinduction\r\n* Refractory to hypomethylating agents

Patients must have had a previous auto-SCT performed as part of a consolidation of an initial remission and had a remission, defined as a partial response or greater that lasted at least 12 months either on or off maintenance therapy without evidence of progression as defined by IMWG criteria

Patients must meet one of two disease criteria:\r\n* Acute myelogenous leukemia within one of the following categories:\r\n** Primary induction failure (PIF): patients who have not achieved a complete remission following initial diagnosis and after at least two induction cycles of chemotherapy consisting of cytarabine and an anthracycline or high-dose cytarabine\r\n** Relapsed AML: Patients are defined as having relapsed disease if they entered a complete remission confirmed with a bone marrow biopsy following initial treatment, and then were found to have morphological or cytogenetic evidence of recurrent disease on a subsequent bone marrow exam\r\n** Any complete remission (CR)2 or greater: CR must be defined using a bone marrow exam taken at least 21 days since the last chemotherapy (including a methyltransferase inhibitor), and may include CRp (morphologic CR without peripheral platelet recovery)\r\n** CR1 with high-risk features: includes patients with treatment-related AML, secondary AML (following myelodysplastic syndrome [MDS] or myeloproliferative neoplasms [MPN]), high-risk cytogenetic or molecular phenotype (by National Comprehensive Cancer Network [NCCN] criteria)\r\n** Untreated AML (> 20% blasts on a bone marrow) arising from a previous confirmed diagnosis of MDS or MPN (excluding breakpoint cluster region [BCR]-Abelson murine leukemia viral oncogene homolog 1 [ABL] positive disease)\r\n* Myelodysplastic syndromes within one of the following categories:\r\n** High-risk MDS at diagnosis as defined by the International Prognostic Scoring System (IPSS) or World Health Organization (WHO) classification based Prognostic Scoring System (WPSS)\r\n** Transfusion dependent MDS (either red blood cells [RBC] or platelet dependent) without a hematologic response to at least 4 months of MTI therapy; hematological response is defined as transfusion independence for two or more months\r\n** Progressive MDS following at least 4 months of MTI therapy; progression is defined as resumption of transfusion dependence after at least two months of transfusion independence OR increase of marrow blasts by 50% from pretreatment OR overall blasts over 10% of marrow cells at any time after treatment

Acute lymphoblastic leukemia, including biphenotypic acute leukemia or mixed-lineage leukemia\r\n* High risk first complete remission (CR1) (for example, but not limited to: t(9;22), t(1;19), t(4;11) or other mixed-lineage leukemia [MLL] rearrangements, hypodiploid); or high risk (HR) as defined by referring institution treatment protocol greater than 1 cycle to obtain CR; second complete remission (CR2) or greater\r\n* All patients must be in CR as defined by < 5% blasts by morphology/flow cytometry in a representative bone marrow sample with cellularity >= 15% for age\r\n* Patients in which adequate marrow/biopsy specimens cannot be obtained to determine remission status by morphologic assessment, but have fulfilled criteria of remission by flow cytometry, recovery of peripheral blood counts with no circulating blasts, and/or normal cytogenetics (if applicable) may still be eligible; reasonable attempts must be made to obtain an adequate specimen for morphologic assessment, including possible repeat procedures; these patients must be discussed with the principal investigator prior to enrollment

Diagnosis of high risk hematological malignancy:\r\n* Any acute leukemia in first complete remission (CR) considered at high risk for relapse, or second or third CR, or relapse/refractory less than 10% blasts in bone marrow, or aplasia post-therapy; this includes de novo acute leukemia or acute leukemia that is therapy related or arising from an antecedent hematologic disorder including myelodysplasia (MDS), chronic myeloid leukemia (CML) or other myeloproliferative disorder\r\n* Juvenile myelomonocytic leukemia (JMML) in CR, or relapse with less than 10% bone marrow blasts \r\n* CML with tyrosine kinase inhibitor failure in chronic or accelerated phase or evolved to acute leukemia (blast crisis, see above)\r\n* MDS or other myeloproliferative disorder with life-threatening cytopenia(s), and/or red blood cell or platelet transfusion dependence, or patients with aplasia, or patients with excess blasts less than 10% blasts in the bone marrow at work-up\r\n* Aggressive lymphoma: patients in first complete remission (CR1) with disease at high risk of relapse or CR2-3 \r\n* Indolent lymphoma or chronic lymphocytic leukemia (CLL): any disease status provided any transformed component is in CR\r\n* Hodgkin lymphoma that is primary refractory or relapsed not suitable for other therapy and in partial remission (PR) or CR or small volume stable disease

Enrolled in University Of Minnesota study MT2001-10 “Allogeneic Bone Marrow Transplantation Using Less Intensive Therapy” and fitting into one of the following disease categories:\r\n* Acute myelogenous leukemia - high risk first complete remission (CR1) (as evidenced by preceding myelodysplastic syndrome [MDS], intermediate to high risk cytogenetics, >= 2 cycles to obtain complete remission (CR), erythroblastic or megakaryocytic leukemia; second complete remission (CR2)+; all patients must be in CR as defined by hematological recovery (absolute neutrophil count [ANC] > 0.5 x 10^9/L), AND < 5% blasts by light microscopy within the bone marrow with a cellularity of >= 15%\r\n* Acute lymphocytic leukemia - high risk CR1 [t(9;22), t (1:19), t(4;11) or other mixed-lineage leukemia [MLL] rearrangements] or > 1 cycle to obtain CR; CR2+; all patients must be in CR as defined by hematological recovery (ANC > 0.5 x 10^9/L), AND < 5% blasts by light microscopy within the bone marrow with a cellularity of >= 15%\r\n* Chronic myelogenous leukemia all types except blast crisis (note treated blast crisis in chronic phase is eligible)\r\n* Non-Hodgkin lymphoma or Hodgkin’s lymphoma demonstrating chemosensitive disease\r\n* Myelodysplastic syndrome with severe pancytopenia, leading to either transfusion dependency or increased risk for infections

High-risk disease as defined by one of the following: \r\n* First relapse after CR within 12 months of initiation of front-line therapy \r\n* Less than CR to front-line therapy \r\n* Second-line Age-Adjusted International Prognostic Index (sAAIPI) of 2 or higher at the time of relapse

The patient has pathologically documented AML and is in CR1 at the time of the screening visit

The patient achieved CR1 within 10 weeks of the screening visit; the patient may have received post-remission consolidation therapy (except for transplant) prior to the screening visit

Cohorts 1 and 3: Participants must have stable disease or be responders (partial response [PR] or complete response [CR]) to neratinib in the CNS at the time of non-CNS progression

CLL patients with evidence of residual disease, who have achieved partial response (PR), nodular partial response (nPR) or complete response (CR) with detectable minimal residual disease (MRD) following upfront therapy consisting of pentostatin, cyclophosphamide and rituximab\r\n* The presence of MRD will be assessed by the flow cytometry and polymerase chain reaction at the Memorial Sloan Kettering Cancer Center (MSKCC) Diagnostic Molecular Pathology Laboratory

Primary AML induction failure: no complete remission (CR) after 2 or more induction attempts

Relapsed AML or secondary AML (from myelodysplastic syndromes [MDS] or treatment related): not in CR after 1 or more cycles of standard re-induction therapy

Acute myeloid leukemia (AML) fitting within one of the following disease groups:\r\n* Primary induction failure (PIF): patients who have not achieved a complete remission (CR) after two induction cycles of cytotoxic therapy (i.e. 7+3, mitoxantrone, etoposide, and cytarabine [MEC], fludarabine, cytarabine, and granulocyte-colony stimulating factor [FLAG], etc.) and having =< 10,000 absolute circulating blasts measured at least 21 days from prior therapy; hydroxyurea may be used to control blasts count; demethylating agents do not count as induction therapy; however early re-induction therapy based on residual disease on a day 14 bone marrow (BM) will count as a 2nd cycle\r\n* Relapsed disease with low disease burden: AML with =< 10,000 absolute circulating blasts; hydroxyurea may be used to control blasts count: no re-induction attempts are required, but a maximum of 2 re-induction attempts is allowed to be eligible\r\n* CR3 or greater: this will include CRp defined as CR without platelet recovery to 100,000/mcL\r\n* CR1 or CR2 with high risk features: includes therapy induced, prior myelodysplastic syndromes (MDS) or myeloproliferative disease (MPD), high risk cytogenetic or molecular phenotype with no available donor (sibling or unrelated adult)

Acute lymphocytic leukemia\r\n* Adult: (>= 22 years) >= second complete remission (CR2) OR first CR (CR1) with a high risk feature:\r\n** Matched sibling donor for recipient treated on adult leukemia regimen\r\n** t(9:22) or breakpoint cluster region (bcr)-Abelson (abl)+; t(4:11), t(1:19), t(8:14), 11q23 (mixed lineage leukemia [MLL] rearrangements) complex cytogenetics (5 or more chromosomal abnormalities), hypodiploidy (< 44 chromosomes.; note that patients with acute lymphoblastic leukemia (ALL) blast crisis who emerge from chronic myelogenous leukemia (CML) are also eligible\r\n** Primary induction failure, defined as failure to achieve CR with primary induction chemotherapy\r\n** High white blood cell (WBC) (> 30,000 for B-cell ALL and > 100,000 for T-cell ALL) at diagnosis\r\n** Persistence of minimal residual disease despite induction chemotherapy\r\n* Pediatric (< 22 years): >= CR2 OR CR1 with high risk features\r\n** Matched sibling donor for recipient treated on adult leukemia regimen\r\n** Primary induction failure (M3 [> 25% with greater 200 cells counted] marrow at day 29), M2 (5-25% blasts with greater than 200 cells counted) bone marrow or minimal residual disease (MRD) > 1% at day 29 who then fail at day 43 with either M2 or M3 bone marrow (BM) or MRD > 1%\r\n** Persistent leukemia and t(9;22) (MRD > 1% day 29 or MRD > 0.01% end-consolidation)\r\n** 11q23 (MLL) rearrangements detected by cytogenetic or polymerase chain reaction (PCR) at initial diagnosis who are slow early responders (M2/M3 at day 14 or MRD > 0.01% at day 29)\r\n** Extreme hypodiploidy (< 44 chromosomes or deoxyribonucleic acid [DNA] index of < 0.81) detected by cytogenetic/ploidy analysis

Acute myelogenous leukemia\r\n* Adult: (>= 22 years) >= CR2 OR CR1 with one of the following high risk features\r\n** Adverse or intermediate-risk cytogenetics including:\r\n*** Normal cytogenetics\r\n*** Complex karyotype (> 2 abnormalities)\r\n*** Inv (3) or t(3;3); t(11;19)(q23;p13.1); +13; -17/17p-; -18; -20; (t(6;9); t(6;11); -7, 7q-; -5, 5q-; trisomy 8; t(3;5); t(9:11)(p22q23)\r\n*** Monosomy karyotype (presence of an autosomal monosomy in conjunction with at least one other autosomal monosomy or structural abnormality\r\n*** Any other karyotype EXCEPT t(8;21), t(9;11), inv(16), or t(16;16), and M3 (17; 17) unless v-kit Hardy-Zuckerman 4 feline sarcoma viral oncogene homolog (c-Kit) mutation present and then eligible\r\n*** AML emerging from CML (blast crisis) are eligible\r\n** Primary induction failure, defined as failure to achieve CR with primary induction chemotherapy\r\n** Secondary AML, defined as AML related to antecedent myelodysplastic syndrome (MDS), myeloproliferative neoplasm (MPN), or cytotoxic chemotherapy\r\n** Hyperleukocytosis (white blood cells [WBC] > 100,000 at diagnosis)\r\n** Mutations in the FMS-like tyrosine kinase 3 (FLT3) gene (FLT3-length mutations [LM]; FLT-internal tandem duplications [ITDs])\r\n** Bilineage or biphenotypic leukemias are high risk features and eligible\r\n* Pediatric (< 22 years): >= CR2 OR CR1 with a high risk feature including\r\n** Primary induction failure (>= 5% blasts in marrow after induction)\r\n** Persistent leukemia (> 15% after first course of chemotherapy)\r\n** Complex karyotype monosomy 7, or -5/-5q, FLT3 ITD-allelic ratio (AR) (> 0.4) EXCEPT if also inv(16)/t(16;16), t(8,21)\r\n** Normal cytogenetics or abnormal cytogenetics EXCEPT if also inv(16)/t(16;16), t(8,21) are eligible for SIBLING transplant only\r\n** Bilineage or biphenotypic leukemias are high risk features and eligible

Patients must have partial remission (PR) to salvage chemotherapy

Patients must have advanced AML, ALL or high-risk MDS meeting one of the following descriptions:\r\n* AML or ALL beyond first remission (i.e., having relapsed at least one time after achieving remission in response to a treatment regimen)\r\n* AML or ALL representing primary refractory disease (i.e., having failed to achieve remission at any time following one or more prior treatment regimens)\r\n* AML evolved from myelodysplastic or myeloproliferative syndromes; or \r\n* MDS expressed as refractory anemia with excess blasts (RAEB) or chronic myelomonocytic leukemia (CMML) by French-American-British (FAB) criteria

Patients not in remission must have CD45-expressing leukemic blasts; patients in remission do not require phenotyping and may have leukemia previously documented to be CD45 negative (because in remission patients, virtually all antibody binding is to non-malignant cells which make up >= 95% of nucleated cells in the marrow)

Best response achieved was ?Partial Response (PR)

Prior bendamustine treatment within 1 year of randomization not resulting in a CR or PR for at least 6 months

Patients must have B-ALL refractory, relapsed, minimal residual disease (MRD), or in first complete remission (CR) as described below\r\n* Complete remission is defined as restoration of normal hematopoiesis with a neutrophil count > 1,000 x 10^6/L, a platelet count > 100,000 x 10^6/L, and hemoglobin > 10 g/dL; blasts should be < 5% in a post-treatment bone marrow differential; furthermore, there should be no clinical evidence of leukemia for a minimum of four weeks\r\n* MRD is defined as patients meeting the criteria for CR above, but with residual disease measured by a quantitative polymerase chain reaction (qPCR), or by flow, or by deep-sequencing of the immunoglobulin heavy chain (IgH) rearrangements; the assay from blood and/or bone marrow defines MRD by qPCR as a cycle threshold (CT) that is at least 1 CT value < than the lowest CT value from the background; outside laboratory tests may suffice for this assessment at the discretion of the principal investigator\r\n* Relapsed B-ALL will be defined as patients that meet the above criteria for a CR before developing recurrent disease (increased bone marrow blasts); refractory patients will be defined as patients that have not achieved a CR after 1 cycle of induction chemotherapy

For subjects Age < 65\r\n* Refractory AML\r\n* OR AML relapse within six months of attaining remission\r\n* OR AML relapse more than six months after achieving a remission, who cannot achieve a second remission \r\n* OR Untreated subjects who develop AML after preexisting hematologic disease \r\n* OR Secondary AML\r\nFor subjects Age >= 65\r\n* De novo AML not candidates for induction chemotherapy\r\n* OR Refractory AML\r\n* OR AML relapse within six months of attaining remission\r\n* OR AML relapse more than six months after achieving a remission, who cannot achieve a second remission\r\n* OR Untreated subjects who develop AML after preexisting hematologic disease \r\n* OR Secondary AML

Biphenotypic leukemia that at the time of allogeneic transplantation was in induction failure, relapsed disease, first, second or greater remission

Patients must be in complete remission post transplant

Acute myelogenous leukemia (AML) in induction failure, relapse, past first remission, or first complete remission (CR1) considered at risk for relapse

Acute lymphocytic leukemia with induction failure, first complete remission with high risk cytogenetics (e.g. Philadelphia positive chromosome, t[4:11]; remission requiring more than 2 chemotherapy to achieve remission, or any stage beyond CR1

Hodgkin's disease - induction failure, second or later complete remission, or relapse (including relapse post autologous hematopoietic stem cell transplant)

Mantle cell NHL must be beyond first complete response (CR)

Must have achieved a minimum response of partial response (PR, nPR, CRi, CR, and MRD-negative CR) (IWCLL guidelines for the diagnosis and treatment of chronic lymphocytic leukemia [Hallek, 2008]) following completion of second-line induction therapy prior to randomization (documentation of response status must be available). Second-line induction therapy must be documented to have been of sufficient duration.

Patients not in remission must have cluster of differentiation (CD)45-expressing leukemic blasts; patients in remission do not require phenotyping and may have leukemia previously documented to be CD45 negative (because in remission patients, virtually all antibody binding is to non-malignant cells which make up >= 95% of nucleated cells in the marrow)

Acute myelogenous leukemia\r\n* In first complete remission with high-risk cytogenetics\r\n* Primary induction failure\r\n* In second or greater complete remission\r\n* Secondary AML\r\n* In first complete remission with hyperleukocytosis at diagnosis

Acute lymphocytic leukemia\r\n* First complete remission, with high-risk cytogenetics\r\n* Primary induction failure\r\n* Second or greater complete remission

NK cell neoplasms\r\n* First complete remission (CR) for patients with high risk natural killer cell neoplasms including myeloid/NK cell precursor acute leukemia, blastic NK-cell lymphoma, aggressive NK-cell leukemia and nasal-type extranodal NK-cell lymphoma in first complete remission\r\n* Primary induction failure\r\n* Second or greater CR

Recipients with AML in first complete remission (CR1) must have one of the following:\r\n* Adverse cytogenetics with residual disease detectable by flow cytometry, cytogenetic analysis, fluorescence in situ hybridization (FISH), or polymerase chain reaction (PCR); adverse cytogenetics in AML are defined as complex karyotype (>= 3 abnormalities); inversion (inv)(3) or t(3;3); t(6;9); t(6;11); monosomy 7; trisomy 8, alone or with an abnormality other than t(8;21), t(9;11), inv(16) or t(16;16); or t(11;19 (q23;p13.1) \r\n* Primary induction failure, defined as failure to achieve CR with primary induction chemotherapy \r\n* Secondary AML, defined as AML related to antecedent MDS, MPD, or cytotoxic chemotherapy\r\n* Hyperleukocytosis, white blood cells (WBC) >= 100,000, at diagnosis\r\n* Mutations in the FMS-like tyrosine kinase 3 (FLT3) gene (FLT3-LM; FLT internal tandem duplication [ITD]s)

Recipients with ALL in CR1 must have one of the following:\r\n* Adverse cytogenetics or residual disease detectable by flow cytometry, cytogenetic analysis, FISH, or PCR; adverse cytogenetics in ALL are defined as translocations involving t(4;11), t(1;19), t(8;14), 11q23, t(9;22) or bcr-abl rearrangement or complex cytogenetic abnormalities\r\n* Primary induction failure, defined as failure to achieve CR with primary induction chemotherapy

Acute lymphoblastic leukemia (ALL): induction failure, primary refractory to treatment (do not achieve complete remission after first course of therapy) or are beyond first remission including second or greater remission or active disease; patients in first remission are eligible if they are considered high risk, defined as any of the following detected at any time: with translocations 9;22 or 4;11, hypodiploidy, complex karyotype, secondary leukemia developing after cytotoxic drug exposure, and/or evidence of minimal residual disease, or acute biphenotypic leukemia, or double hit non-Hodgkin's lymphoma; or

Hodgkin's disease (HD): induction failures, second or third complete remission, or relapse (including relapse post autologous hematopoietic stem cell transplant); or

Relapse after achieving initial remission or failure to achieve initial remission

Diagnosis of one of the following: Previously untreated Ph-positive ALL [either t(9;22) and/or bcr-abl positive] (includes patients initiated on first course of hyper-CVAD before cytogenetics known) These groups will be analyzed separately. After 1-2 courses of chemotherapy with or without imatinib mesylate (Gleevec) · If they achieved CR, they are assessable only for event-free and overall survival, or · If they failed to achieve CR, they are assessable for CR, event-free, and overall survival. Patients with relapsed Ph-positive ALL or lymphoid blast phase of CML.

Creatinine (Cr) =< 2.0

Patients must have histologically confirmed relapsed or refractory AML and meet the following criteria:\r\n* Relapsed disease is defined as AML is in 1st or greater marrow relapse\r\n* Refractory disease is defined as AML which failed to go into remission after 1st or greater relapse, OR AML which failed to go into remission after two or more induction attempts from original diagnosis

Adequately treated Stage I cancer from which the subject is currently in remission and has been in remission for ?2 years

Recurrent, and/or metastatic germline BRCA 1/2 mutation-associated ovarian cancer, with progression on a PARP inhibitor monotherapy after attaining a response to that PARPi (CR, PR, or stable disease [SD] >= 4 months [mo])

Refractory B-ALL, defined by not having achieved a CR or CRi after two attempts at remission induction using standard regimens, or

Acute myeloid leukemia (AML) in >= first (1st) remission - excluding those in 1st remission with ‘good risk’ cytogenetic features (i.e. t(8;21), t(15;17), inv 16)

Non-Hodgkin's lymphoma with chemoresponsive disease in any of the following categories: \r\n* High grade lymphomas who have failed to achieve a first CR or have relapsed following a 1st remission who are not candidates for autologous transplants or transplants requiring the use of calcineurin inhibitors\r\n* Any NHL with therapy responsive disease which is considered not curable outside the transplant setting and not eligible/appropriate for autologous transplant or a higher priority protocol

Relapse after going into remission from re-induction for the first or subsequent relapse (ie: 2nd , 3rd, 4th…relapse), OR

Failing to go into remission from original diagnosis after 2 previous induction attempts.

Patients to be enrolled in the dose-escalation portion of this study must have T-cell ALL or T-cell lymphoblastic lymphoma (LL) in first relapse or must have failed primary induction chemotherapy (ie, never attained a complete remission following an initial course of standard therapy for T-ALL or T-LL). Patients to be enrolled in the cohort expansion portion of this study (ie, those treated at the recommended phase 2 dose) must have T-cell ALL in first relapse or must have failed primary induction chemotherapy (ie, never attained a complete remission following an initial course of standard therapy for T-ALL). T-LL patients are not eligible for the cohort expansion phase.

Patient should have a responsive skin disease including complete remission (CR) and partial remission (PR) (close to CR; 75%-99% clearance of skin disease from baseline without new tumors (T3) in patients with T1, T2 or T4 only skin disease) and should not have visceral organ or lymph node involvement prior to transplantation

Acute Myelogenous Leukemia (AML) in high risk 1st or subsequent CR

Biphenotypic or undifferentiated leukemia in 1st or subsequent CR

Patient must have documented CR or CRp after 1 or 2 cycles of fludarabine + cytarabine

One of the following:\r\n* Acute leukemia past first remission, in first or subsequent relapse, in second or greater remission; patients in first remission should have with intermediate or high cytogenetic risk factors or fms-related tyrosine kinase 3 (flt3) mutation; patients with relapsed disease; patients with primary induction failure or relapse are eligible if they have < 10% bone marrow blasts, and no circulating blasts\r\n* Myelodysplastic syndrome with intermediate or high risk International Prognostic Scoring System (IPSS) score, or treatment related myelodysplastic syndrome (MDS)\r\n* Chronic myeloid leukemia (CML) resistant to tyrosine kinase treatment in a first or subsequent chronic phase or after transformation to accelerated phase or blast crisis\r\n* Chronic lymphocytic leukemia (CLL), lymphoma or Hodgkin’s disease which has failed to achieve remission or recurred following initial chemotherapy; patients must have at least a PR to salvage therapy, or low bulk untreated relapse (< 2 cm largest mass)\r\n* Multiple myeloma which has relapsed or progressed and has achieved a partial response to salvage chemotherapy

A confirmed baseline diagnosis of AML by the revised guidelines of the International Working Group for AML including newly diagnosed, relapsed or refractory disease\r\n*Newly diagnosed: \r\n** Age 70 years and older \r\n** 60-69 years old and unfit for conventional chemotherapy\r\n* Relapsed disease: \r\n** Age 60 years and older any time following the first relapse, if the patient is not considered candidate for or is not interested in salvage chemotherapy\r\n** Age 18-59 years who have relapsed less than 6 months following achievement of a complete remission (defined as duration of remission from the time of documentation of complete morphologic remission to the time of documentation of relapse)\r\n* Refractory disease: \r\n** Age 18-59 years who have failed at least two lines of conventional chemotherapy (one induction and one salvage therapy); examples include: \r\n*** Patient achieves a complete remission and receives (or does not receive) consolidation therapy, but relapses later; this patient will be eligible only if s/he fails at least one salvage therapy following relapse\r\n*** Patient demonstrates residual leukemia on post-induction day 14 bone marrow and receives salvage therapy; this patient will be eligible only if s/he fails the salvage therapy\r\n*** Patient demonstrates reasonable response on post-induction day 14 bone marrow (or the bone marrow is not performed), but the follow-up bone marrow shows residual disease; this patient will be eligible only if s/he fails at least one salvage therapy\r\n** Age 60 and older who have failed at least one line of conventional chemotherapy, or treatment with hypomethylating agent (in the setting of poor-risk/complex karyotype) and is not considered candidate for or is not interested in salvage chemotherapy; FltITD +ve disease is not considered responsive to hypomethylating agent\r\n* Patients age 18 years and older with relapse in the form of AML after stem cell transplant will be eligible, even if they were transplanted for myelodysplastic syndromes (MDS) or myeloproliferative neoplasm (MPN)

Patients with a history of any other cancer, unless in complete remission, and off all therapy for that disease for a minimum of 5 years

Patient has achieved CR or partial response (PR) per per investigator's assessment following completion of CHOP-based therapy and has had radiological assessment within 21 days prior to randomization.

ALCL (ALK+) with IPI score less than 2 at initial diagnosis and CR after CHOP-based therapy

No evidence of progressive disease following completion of first-line chemotherapy (i.e., ongoing CR, PR, or SD per RECIST v1.1 guidelines )

Must be within 75 days of completion of first-line treatment regimen; must have achieved complete response (CR/unconfirmed complete response [CRu]) to first-line treatment

If CSF was positive for lymphoma cells at diagnosis or during first-line treatment and/or a slit lamp examination was positive at diagnosis or during first-line treatment, then the CSF and vitreal studies must have been repeated and must have indicated CR; Note: CR requires complete disappearance of all enhancing abnormalities on gadolinium-enhanced MRI; if CSF was positive for lymphoma cells at diagnosis or during first-line treatment and/or slit lamp examination was positive at diagnosis or during first-line treatment, then the CSF and vitreal studies must have been repeated and must have indicated CR; for CRu, some patients will have a small but persistent enhancing abnormality on MRI related to biopsy or focal hemorrhage; it is often difficult to ascertain whether this represents a residual nidus of tumor or scar tissue; if the abnormality does not change or slowly involutes without therapy and corticosteroids, it is reasonable to categorize as a CRu; at the time CR/CRu is determined, the patient should not have used corticosteroids for at least two weeks

Acute lymphoblastic leukemia \r\n* >= second complete remission (CR2) (adults >= 18 years and =< 55 years) \r\n* CR2 in pediatrics (defined as < 18 years) and < 12 months duration of first remission\r\n* >= third complete remission (CR3) or not in remission (pediatric patients < 18 years)\r\n* T cell leukemia >= CR2\r\n* Evidence of pre-transplant minimal residual disease (MRD) by flow cytometry, fluorescence in situ hybridization (FISH) or cytogenetics

Chemotherapy refractory acute leukemia (AL) will be defined by not in achieving a hematological remission after two consecutive standard courses of induction therapy

Multiple myeloma\r\n* No prior auto hematopoietic transplantation (HCT) fitting into one of the following categories:\r\n** Early disease stage (first complete response [CR1]/first partial response [PR1]) with high-risk molecular features:\r\n*** By FISH or cytogenetics:\r\n**** t(4;14)\r\n**** t(14;16) \r\n**** t(14;20)\r\n**** -17 or -17p\r\n**** -1p or +1q\r\n*** By cytogenetics:\r\n**** -13 or -13q\r\n*** By gene expression profile (GEP):\r\n**** High risk GEP\r\n** Early disease stage (CR1/PR1) with high-risk clinical features:\r\n*** Plasma cell leukemia at presentation\r\n*** Poor count recovery after chemotherapy, making collections from autologous HCT unlikely to be adequate\r\n** Late disease stage (CR2/second partial response [PR2+]) with high- risk clinical features\r\n*** Minimal (< 50% reduction of serum M protein or free light chains, or if non-secretory, < 50% reduction in marrow plasma cell burden) response or progression after therapy with at least two novel agents, including lenalidomide and bortezomib, who demonstrates chemosensitivity to any other salvage regimen\r\n*** Poor count recovery after chemotherapy, making collections for autologous HCT unlikely to be adequate

Individuals who have undergone transplant for hematologic malignancy are required to be in complete remission.

Relapsed or refractory AML, defined as either: recurrence of disease after a complete remission (CR), or failure to achieve CR with initial therapy.

Part specific requirements: eligible to receive induction; achieved CR/CRi with standard induction and eligible to receive consolidation; in CR with documented blood count recovery for maintenance

Patients must have one of the following hematologic malignancies: \r\n* Acute myelogenous leukemia (AML), induction failure, high-risk for relapse first remission (with intermediate-risk or high-risk cytogenetics, fms-like tyrosine kinase [flt]3 mutation positive and/or evidence of minimal residual disease by flow cytometry), secondary leukemia from prior chemotherapy and/or arising from myelodysplastic syndrome (MDS), Langerhans cell histiocytosis, any disease beyond first remission; or\r\n* Myelodysplastic syndrome (MDS): primary or therapy related; or\r\n* Acute lymphoblastic leukemia (ALL): induction failure, primary refractory to treatment (do not achieve complete remission after first course of therapy) or are beyond first remission including second or greater remission or active disease; patients in first remission are eligible if they are considered high risk, defined as any of the following detected at any time: with translocations 9;22 or 4;11, hypodiploidy, complex karyotype, secondary leukemia developing after cytotoxic drug exposure, and/or evidence of minimal residual disease, or acute biphenotypic leukemia, or double hit non-Hodgkin's lymphoma; or \r\n* Non-Hodgkin's lymphoma (NHL): in primary induction failure, second or third complete remission, refractory disease, or relapse (including relapse post autologous hematopoietic stem cell transplant); double hit lymphomas in first remission or more advanced disease; or \r\n* Small lymphocytic lymphoma (SLL), or chronic lymphocytic leukemia (CLL) with progressive disease following standard therapy; or,\r\n* Chronic myelogenous leukemia (CML) second chronic phase or accelerated phase; or,\r\n* Hodgkin's disease (HD): induction failures, second or third complete remission, or relapse (including relapse post autologous hematopoietic stem cell transplant)

Subjects who are refractory* or who have relapsed** following first line AML therapy with cytarabine/anthracycline based chemotherapy, with or without a tyrosine kinase inhibitor. *Refractory to induction therapy is defined as never achieving CR, CRi or CRp (according to International Working Group criteria) after one line of intensive regimen for AML (re-induction, consolidation and/or transplant allowed) including at least one cytarabine containing induction block with a total dose no less than 700mg/m² per cycle and 3 days of an anthracycline with or without a TKI. or **First relapse is defined as untreated hematologic relapse (according to International Working Group criteria) after one line of intensive regimen for AML (re-induction, consolidation and/or transplant allowed) including at least one cytarabine containing induction block with a total dose no less than 700mg/m² per cycle and 3 days of an anthracycline with or without a TKI that induced a CR/CRi/CRp. Subjects are allowed to receive induction, consolidation, transplant and/or maintenance prior to achieving their first CR/CRi/CRp.

Any curable cancer with a complete response (CR) of > 5 years duration.

Individuals with PMF, post-PV MF, or post-ET MF who are receiving ruxolitinib and meet 2013 Revised International Working Group for Myelofibrosis Research and Treatment (IWG-MRT) and European Leukemia Net (ELN) response criteria with progressive and relapsed disease, with modifications for progressive disease complete remission (CR), partial remission (PR), or clinical improvement (CI)

High-risk hematologic malignancy\r\n* Very high risk acute lymphocytic leukemia (ALL) in first complete remission (CR1); examples include, but not limited to hypodiploid M2 or greater marrow at the end of induction, infants with mixed lineage leukemia (MLL) fusion or t(4;11)\r\n* ALL in high risk second complete remission (CR2); examples include but not limited to bone marrow (BM) relapse < 36 months (mo); CR1, T-ALL, very early (< 6 mo CR1) isolated central nervous system (CNS) relapse\r\n* ALL in third complete remission (CR3) or subsequent\r\n* Acute myeloid leukemia (AML) in high risk CR1; examples include but not limited to preceding myelodysplastic syndromes (MDS), 5q-, -5, -7, French American British (FAB) M6, FAB M7 not t(1;22), minimal residual disease (MRD) >= 5% on day 22 (AML08), M3 marrow after induction 1, M2 marrow after two cycles of induction, fms-related tyrosine kinase 3 (FLT3)-internal tandem duplication (ITD)\r\n* AML in CR2 or subsequent\r\n* Therapy related AML, with prior malignancy in CR > 12 mo\r\n* MDS, primary or secondary\r\n* NK cell, biphenotypic, or undifferentiated leukemia in CR1 or subsequent\r\n* Chronic myelogenous leukemia (CML) in accelerated phase, or in chronic phase with persistent molecular positivity or intolerance to tyrosine kinase inhibitor\r\n* Hodgkin lymphoma in CR2 or subsequent after failure of prior autologous HCT, or unable to mobilize stem cells for autologous HCT\r\n* Non-Hodgkin lymphoma in CR2 or subsequent\r\n* Juvenile myelomonocytic leukemia (JMML)\r\n* Refractory hematologic malignancies (ALL, AML, CML in blast crisis, Hodgkin or non-Hodgkin lymphoma) due to chemoresistant relapse or primary induction failure\r\n* All patients with evidence of CNS leukemia must be treated and be in CNS CR to be eligible for study

Creatinine (Cr) > 2.5

Relapsed after achieving remission with a prior therapy

Patients with a complete response (CR) to their previous regimen must have a cancer antigen (CA)-125 within normal range; this criterion is not applicable to patients who enroll with a partial response (PR) to their previous regimen

Prior or concurrent invasive malignant disease, unless in complete remission for more than three years.

Either achieved complete remission (greater than 12 weeks in duration) with initial induction/consolidation and have experienced relapse of disease or declined treatment with high-dose induction/consolidation

Patients may be registered for consolidation provided that they were eligible for the initial induction/re-induction registration and satisfy the following additional criteria:\r\n* Patients must have achieved morphologic remission (complete remission [CR] or complete remission with incomplete blood count recover [CRi]) after completion of induction or re-induction therapy; patient must remain in remission until beginning consolidation and this must be documented by bone marrow and peripheral blood examination within 28 days prior to registration to Step 2\r\n* All non-hematologic treatment related toxicities that are deemed clinically significant by the treating physician must have resolved to =< grade 2\r\n* Patients must not have received allogeneic stem cell transplant

The patient has achieved a first or second CR or CRi. For patients without evidence of MRD in CR/CRi, CR (or CRi) must have been initially identified within 12 months prior to screening. OR The patient has achieved first or second CR or CRi with evidence of MRD as determined locally at least 6 months post stem cell transplant without evidence of acute or chronic graft-versus-host disease post-transplant and has not received immunosuppressant therapy for at least 14 days prior to SL-401 therapy.

The patient has adverse risk disease or AML for which there is otherwise a substantial risk of relapse, which includes but is not limited to: adverse karyotype, FLT3 internal tandem duplication (ITD) mutation, history of antecedent hematologic disorder (AHD), therapy-related AML, history of requiring more than 1 cycle of intensive induction chemotherapy to achieve first remission, and/or presence of persistent MRD (detected by cytogenetics, molecular markers, or flow cytometry) at any point after the initial induction cycle.

Acute myelogenous leukemia (AML) in first remission that required more than 1 cycle of treatment to achieve remission or with the following cytogenetic abnormalities: FLT3 mutation, deletion/monosomy of chromosome 5 or 7, MLL gene rearrangement, or more than or equal to 3 cytogenetics abnormalities; also patients in second or greater remission

Completed and recovered from all planned induction and consolidation therapy according to the institution's standard of care, and achieved a complete remission (CR)/CR with incomplete platelet recovery (CRp); either first or second CR.

Patient must be either primary refractory to one frontline induction therapy or relapsed after one frontline induction therapy; patients who do not achieve complete remission after induction therapy are also eligible

Refractory disease is defined by the failure to obtain a complete remission (CR) with a HDAC-containing or a standard induction regimen. Patients who require two cycles of induction therapy to attain a first CR are not considered to have refractory disease.

Subjects who have received prior bendamustine are eligible if they achieved a response (CR/PR) which lasted > 6 months after the end of bendamustine containing treatment.

Cr ? 2X ULN

Cr ?2X the ULN

Partial Remission (PR)

Morphologic complete remission with incomplete blood count recovery (CRi)

Acute lymphocytic leukemia (ALL) in first complete remission (CR1) with high-risk features including adverse cytogenetics such as t(9;22), t(1;19), t(4;11), or mixed-lineage leukemia (MLL) gene rearrangements; ALL in second or greater remission or ALL with relapsed disease, peripheral blood blasts < 1000/microliter, ALL patients must show response to most recent received chemotherapy

Acute myeloid leukemia (AML) in CR1 with intermediate-risk disease or high-risk features defined as: \r\n* Greater than 1 cycle of induction therapy required to achieve remission\r\n* Preceding myelodysplastic syndrome (MDS) or myeloproliferative disease\r\n* Presence of fms-related tyrosine kinase 3 (FLT3) mutations or internal tandem duplications\r\n* French-American-British (FAB) M6 or M7 classification\r\n* Adverse cytogenetics, -5, del 5q, -7, del7q, abnormalities involving 3q, 9q, 11q, 20q, 21q, 17, +8 (> 3 abnormalities), peripheral blood blasts < 1000/microliter, AML patients must show response to most recent received chemotherapy

Patients must have had a significant response to standard frontline therapy judged as a complete response or a very good partial response (especially for irradiated sites where complete response [CR] is often impossible to ascertain); clear evidence for persistent or progressive cancer or the administration of a salvage regimen for persistent or progressive disease precludes enrollment on Cohort 2; administration of consolidation such as autologous stem cell transplant without evidence for persistent or progressive disease does not preclude enrollment

The patient is in complete remission (i.e. CR1, CR2, …):

The patient is in morphologic leukemia-free state or in morphologic complete remission with incomplete blood count recovery (CRi).

Hodgkin disease (HD)\r\n * Patients with HD will be eligible if they fail to achieve a CR following conventional therapy\r\n * Patients who relapse following conventional therapy, but fail to achieve a second CR (or for any other reason cannot undergo autologous transplantation) will be eligible\r\n * Patients who relapse after an autologous transplant will be eligible

Acute lymphoblastic leukemia (ALL) \r\n * ALL patients will be eligible if they fail to attain an initial remission, if they relapse within 1 year following the discontinuation of chemotherapy, or if they have other unfavorable prognostic features such that a stem cell transplant (SCT) would offer a significant survival advantage; patients must be in complete remission or have =< 25% blasts in bone marrow at the time of admission to the HSCT unit; patients in complete remission will preferentially receive a myeloablative transplant from a related or unrelated donor; however, patients will be eligible for this study if a suitable related or unrelated donor cannot be identified, the amount of time required to identify a suitable donor is deemed unacceptable, or the patient is not eligible for a myeloablative transplant regimen\r\n * Patients who relapse following a myeloablative transplant, but cannot receive DLI (e.g. cord blood recipients, graft loss) will also be eligible; such patients must be >= 6 months post initial transplant, achieve a CR or have =< 25% blasts in the bone marrow prior to admission to the HSCT unit

Patients with: diffuse large B-cell lymphoma (DLBCL) with one of the following:\r\n* Primary refractory (no complete response [CR] to 1st line); \r\n* High-risk relapse (CR1 < 6 months, secondary international prognostic index [IPI] > 1 or high lactate dehydrogenase [LDH]); or, \r\n* Refractory relapse: no response (stable disease [SD] or progressive disease [PD]) to >= 1 line of salvage

Hodgkin’s with one of the following: \r\n* Primary refractory (no CR to 1st line or PD within 3 months);\r\n* High-risk relapse (CR1 < 1 year, extranodal relapse or B symptoms); or, \r\n* Refractory relapse: no response (SD or PD) to >= 1 line of salvage

Refractory patients:\r\n* Patients must have received at least two attempts at remission induction, which may consist of up to two different therapy courses; Children's Oncology Group (COG) AAML1031 de novo therapy including induction I and induction II is one remission attempt

At least a partial remission before allo-SCT

Patients with multiple myeloma who have not achieved a complete remission (CR) following at least 4 cycles of induction therapy

Patients who are in complete remission or have a stable disease

Willingness to participate in CR program

Be in a complete remission.

Hematologic malignancy in complete remission with minimal residual disease (MRD) detectable by conventional cytogenetics, fluorescence in situ hybridization (FISH), flow cytometry, or molecular testing

Patient must have had a complete response (CR)/partial response (PR)/stable disease (SD), 4-6 weeks after completing last fraction of radiation therapy

Patients must meet one of the following:\r\n* Acute myeloid leukemia (AML) in first (1st) remission - for patients whose AML does not have \good risk\ cytogenetic features (i.e. t[8;21], t[15;17], inv 16 without v-kit Hardy-Zuckerman 4 feline sarcoma viral oncogene homolog [c-kit] mutations)\r\n* Acute leukemias of ambiguous lineage in >= 1st remission\r\n* Secondary AML in remission\r\n* AML in >= second (2nd) remission\r\n* Acute lymphoblastic leukemia (ALL) in 1st remission with clinical or molecular features indicating a high risk for relapse; or ALL >= 2nd remission\r\n* Chronic myelogenous leukemia (CML) failing to respond or not tolerating imatinib, dasatinib or nilotinib in first chronic phase of disease; CML in accelerated phase, second chronic phase, or in complete remission (CR) after accelerated phase or blast crisis\r\n* Non-Hodgkin lymphoma (NHL) with chemo responsive disease in any of the following categories:\r\n** Intermediate or high grade lymphomas who have failed to achieve a first CR or have relapsed following a 1st remission who are not candidates for autologous transplants\r\n** Any NHL in remission which is considered not curable with chemotherapy alone and not eligible/appropriate for autologous transplant\r\n* Myelodysplastic syndrome (MDS): refractory anemia (RA)/refractory cytopenia with multilineage dysplasia (RCMD) with high risk cytogenetic features or transfusion dependence, refractory anemia with excess blasts (RAEB)-1 and RAEB-2\r\n* Chronic myelomonocytic leukemia (CMML): CMML-1 and CMML-2

Renal dysfunction (creatinine [Cr] > 1.8)

Must have a high risk hematologic malignancy as defined below; if the patient does not meet defined eligibility requirements as stipulated below, the principal investigator (PI) must be contacted to determine eligibility:\r\n* Acute myeloid leukemia (AML)\r\n** Patients with AML in the first complete remission (CR) with intermediate or high risk disease\r\n** Patients with AML in first CR with high-risk disease as defined by one of the following abnormalities; CR is defined as an M1 marrow (< 5% blasts by morphology), no evidence of extramedullary disease, and an absolute neutrophil count >= 1.0 x 10^9/L; cases where the ANC is < 1.0 x 10^9/L and rising will also be considered; the PI will need to approve such cases for enrollment; complete remissions without platelet recovery (CRp) will be considered complete remissions

Indicators of High-risk Disease are as follows:\r\n*** Fms-related tyrosine kinase 3 (Flt3)/internal tandem duplication (ITD)+ (If quantitative testing was performed, the allelic ratio must be > 0.4)\r\n*** Residual marrow disease (>= 0.1%) detected by multidimensional flow cytometry after completing at least one cycle of induction chemotherapy\r\n*** Secondary AML; if the AML is secondary to treatment for another malignancy, the first malignancy must be in a complete remission\r\n*** High-risk cytogenetic abnormalities: Different high-risk cytogenetic criteria have been defined for adult and pediatric AML; we will, therefore, use two sets of cytogenetic criteria, one based on Children’s Oncology Group (COG) criteria for pediatric patients and one based on Southwestern Oncology Group (SWOG)/Eastern Oncology Group (ECOG) or Medical Research Council (MRC) criteria for adult patients; examples of high-risk cytogenetics: adult patients (>= 21 years): -5/deletion (del) (5q), -7/del (7q), inversion (inv)3q, del (9q), abnormality (abn)11q, abn 20q, abn21q, abn17P, translocation (t)(6;9), t(9;22), complex karyotypes (>= 3 unrelated abnormalities); pediatric patients (< 21 years): -5/del(5q), -7\r\n*** Other abnormalities associated with a higher risk for AML relapse; there are an increasing number of abnormalities being identified that have been associated with an intermediate or high risk of relapse, but have yet to be incorporated into cooperative group risk classification systems; patients with AML characterized by these abnormalities will be considered; the PI will need to approve such cases for enrollment\r\n** Patients with a partial first remission (PR, defined as an M2 marrow (5-19% blasts by morphology), no evidence of extramedullary disease, and an absolute neutrophil count >= 1.0 x 10^9/L; cases where the ANC is < 1.0 x 10^9/L and rising will also be considered; the PI will need to approve such cases for enrollment\r\n** Patients in 2nd or greater complete or partial remission\r\n* Myelodysplastic syndrome\r\n** Adult patients (>= 21 years) with secondary disease or de novo disease that meets criteria for intermediate, high or very high-risk disease based on the Revised International Prognostic Scoring System; Intermediate risk (3.1-4.5 points), high risk (4.6-6 points), very high risk (> 6 points) \r\n** Pediatric patients with myelodysplastic syndrome (MDS), regardless of subtype, will be eligible\r\n* Acute lymphoblastic leukemia (ALL):\r\n** Given the poor prognosis of adults (>= 21 years) with ALL, adults in 1st or greater complete remission will be eligible; CR is defined as an M1 marrow (< 5% blasts), no evidence of extramedullary disease, and an absolute neutrophil count >= 1.0 x 10^9/L; cases where the ANC is < 1.0 x 10^9/L and rising will also be considered; the PI will need to approve such cases for enrollment; complete remissions without platelet recovery (CRp) will be considered remissions\r\n** Given the generally good prognosis of children (< 21 years) with ALL, they will have to meet one of the criteria listed below; additionally, children who are enrolled on a COG ALL trial for newly diagnosed or relapsed disease will have to meet the criteria for bone marrow transplant (BMT) outlined in that trial; CR is defined as an M1 marrow (< 5% blasts), no evidence of extramedullary disease, and an absolute neutrophil count (ANC) >= 1.0 x 109/L; cases where the ANC is < 1.0 x 10^9/L and rising will also be considered; the PI will need to approve such cases for enrollment; complete remissions without platelet recovery (CRp) will be considered remissions\r\n*** In 1st complete remission with a very high risk for relapse:\r\n**** Hyplodiploidy (< 44 chromosomes, as evidenced by the results of routine analysis of G-banded chromosomes, deoxyribonucleic acid (DNA) index (< 0.81), or other appropriate methodology)\r\n**** > 1% residual marrow blasts by flow cytometry at the end of induction\r\n**** > 0.01% residual marrow blasts by flow cytometry at the end of consolidation\r\n**** Early T-Cell Precursor (ETP) phenotype\r\n*** In 2nd complete remission with B-lineage disease after a marrow relapse occurring less than 36 months from diagnosis\r\n*** In 2nd complete remission with T-lineage disease or Philadelphia chromosome positive (Ph+) disease after a marrow relapse occurring at any time\r\n*** In a 2nd complete remission with T-lineage disease after an extra-medullary relapse occurring less than 18 months from diagnosis\r\n*** In 3rd or greater complete remission after a marrow or extramedullary relapse\r\n*** Other indications for transplant in pediatric patients with ALL must be approved by the study PI with a note to file reflecting study team discussion

Patients with acute undifferentiated, biphenotypic, or bilineal leukemia, which is in 1st or greater complete remission (CR) or partial remission (PR):\r\n* Cr will be defined as an M1 marrow (< 5% blasts), no evidence of extramedullary disease, and an absolute neutrophil count >= 1.0 x 10^9/L; cases where the ANC is < 1.0 x 10^9/L and rising will also be considered; the PI will need to approve such cases for enrollment; CR without platelet recovery (CRp) will be considered complete remissions); PR will be defined as an M2 marrow (5-19% blasts), no evidence of extramedullary disease, and an absolute neutrophil count >= 1.0 x 10^9/L); cases where the ANC is < 1.0 x 10^9/L and rising will also be considered; the PI will need to approve such cases for enrollment\r\n* Chronic myelogenous leukemia (CML):\r\n** Chronic phase with resistance to tyrosine kinase inhibitors\r\n** Accelerated phase (development of cytogenetic abnormality in addition to t(9:22), blood blast percentage >= 10, blood basophil percentage >= 20, platelet count < 100,000 X 10^9/L)\r\n** Blast crisis\r\n** 2nd or greater chronic phase\r\n* Acute Lymphoblastic Lymphoma in 2nd or greater complete remission:\r\n** Complete remission includes confirmed complete response (CR) defined as the disappearance of all evidence of disease from all sites for at least 4 weeks; bone marrow and cerebrospinal fluid (CSF) must be normal and any macroscopic nodules in any organs detectable on imaging techniques shall no longer be present; imaging should include positron emission tomography (PET) scanning; CR will also include unconfirmed complete responses defined as a residual lymph node mass > 1.5 cm in greatest transverse diameter that has regressed by > 75% in sum of the products of the greatest perpendicular diameters (SPD), or any residual lesions in organs that have decreased by > 75%, with a negative PET scan, negative bone marrow and CSF\r\n* Peripheral T cell lymphoma (PTCL):\r\n** In first response (must have at least a partial response)\r\n*** PTCL, unspecified\r\n*** Hepatosplenic gamma-delta T cell lymphoma\r\n** Recurrent PTCL (must be treatment sensitive with at least a partial response); if patient has had a previous autologous transplant, the melphalan and fludarabine conditioning regimen must be utilized\r\n** Chronic myelomonocytic leukemia\r\n** Atypical (breakpoint cluster region- abelson murine leukemia viral oncogene homolog 1 [BCR-ABL] negative) chronic myelogenous leukemia\r\n** Hodgkin lymphoma that has recurred or progressed after an autologous BMT\r\n*** Newly diagnosed or recurrent disease initially refractory to intensive chemotherapy; a partial response or better must be achieved prior to transplantation; eligibility of newly diagnosed cases must be discussed with the study principal investigator (PI)\r\n*** Disease that has recurred or progressed after an autologous BMT; salvage chemotherapy must produce a partial response or better; the melphalan and fludarabine conditioning-regimen must be used for these patients\r\n** Non-Hodgkin lymphoma other than lymphoblastic or peripheral T cell lymphoma\r\n*** Newly diagnosed or recurrent disease initially refractory to intensive chemotherapy; a partial response or better must be achieved prior to transplantation; eligibility of newly diagnosed cases must be discussed with the study PI\r\n*** Disease that has recurred or progressed after an autologous BMT; salvage chemotherapy must produce at least a partial response; the melphalan and fludarabine conditioning-regimen must be used for these patients

Spot urine Ca:Cr ratio >0.25 (>250 mg/g creatinine)

(Part B only) Histologically confirmed DLBCL/MCL/FL/PTCL/MF/CLL on the basis of excisional lymph node or extranodal tissue biopsy; diagnosis of relapsed/refractory disease defined as 1) recurrence of disease after a Complete Response (CR), or 2) Partial Response (PR), Stable Disease (SD) at completion of treatment regimen preceding entry into study, subjects must not be candidates for standard therapy, subjects who have not received Stem Cell Translplant (SCT) must be ineligible to receive SCT.

Considered inappropriate for intensive remission induction therapy by an investigator

Patient must be scheduled to undergo stem cell transplantation for one of the following diagnoses: \r\n* Acute myeloid leukemia (AML) in first complete remission (CR1) (first complete remission, CR or CR with incomplete blood count recovery [CRi]) or second complete remission (CR2) (second complete remission, CR or CRi) \r\n* Acute lymphoblastic leukemia (ALL) in CR1 or CR2, (CR or CRi)\r\n* Myelodysplastic syndrome (MDS) without progression to AML \r\n* Chronic myelogenous leukemia (CML)\r\n* Non-Hodgkin’s lymphoma (NHL) or Hodgkin’s disease (HD)\r\n* Chronic lymphocytic leukemia (CLL)\r\n* Multiple myeloma (MM)

Acute Lymphoblastic Leukemia (ALL) in first complete remission (CR1) that is NOT considered favorable-risk as defined by the presence of at least one of the following:\r\n* Adverse cytogenetics such as t(9;22), t(1;19), t(4;11), other mixed lineage leukemia (MLL) rearrangements\r\n* White blood cell counts of greater than 30,000/mcL (B-ALL) or greater than 100,000/mcL (T-ALL) at diagnosis\r\n* Recipient age older than 30 years at diagnosis\r\n* Time to CR greater than 4 weeks

Acute Myelogenous Leukemia (AML) in first complete remission (CR1) that is NOT considered as favorable-risk; favorable risk is defined as having one of the following:\r\n* t(8,21) without CKIT mutation\r\n* inv(16) without CKIT mutation or t(16;16)\r\n* Normal karyotype with mutated nucleophosmin (NPM)1 and not fms-related tyrosine kinase (FLT)-IND\r\n* Normal karyotype with double mutated CCAAT enhancer binding protein alpha (CEBPA)\r\n* Acute promyelocytic leukemia (APL) in first molecular remission at end of consolidation

Acute leukemias in 2nd or subsequent CR

Biphenotypic/undifferentiated in first or subsequent CR, adult T-cell leukemia/lymphoma in first or subsequent CR

Burkitt’s lymphoma in CR2 or subsequent CR

All patients must be in complete remission (CR):

Specific Criteria by Stratum: Stratum 1: All patients must have completed standard upfront therapy that replicates treatment which patients who were enrolled on ANBL0032 received, including: intensive induction chemotherapy and (if feasible) resection of primary tumor, followed by: consolidation with high-dose chemotherapy with stem cell transplant and radiotherapy, followed by: immunotherapy with Ch14.18/IL-2/GM-CSF (dinutuximab) and retinoic acid;. All subjects on Stratum 1 must have also met the following criteria: • A pre-transplant disease status evaluation that met International Neuroblastoma Response Criteria (INRC) for CR (complete response), VGPR (very good partial response), or PR (partial response) for primary site, soft tissue metastases and bone metastases. Patients who meet those criteria must also meet the protocol-specified criteria for bone marrow response prior to transplant as outlined below: No more than 10% tumor involvement (based on total nucleated cellular content) seen on any specimen from a bilateral bone marrow aspirate/biopsy. Stratum 2: Neuroblastoma that is in first complete remission following standard upfront therapy different from that described for Stratum 1. Stratum 3: Neuroblastoma that failed to have a response of at least PR following induction chemotherapy and surgical resection of the primary tumor, but that has achieved CR following additional therapy. Stratum 4: Patients who have achieved a second or subsequent CR following relapse(s).

Patients with benign hematologic disorders such as severe aplastic anemia do not have disease response requirements; patients with a malignant hematologic disorder must be in complete response (CR) (MRD is allowed) with the exception of the following:\r\n* Patients with MDS/MPN only require < 5% myeloblasts on bone marrow evaluation\r\n* Patients with AML or ALL may be in complete remission with incomplete marrow recovery (CRi), patients with MM may be in very good partial response (VGPR)

Acute leukemia in complete remission (CR)1 or second/subsequent CR

Non-Hodgkin lymphoma in high risk CR1 or subsequent CR (by clinical, cytogenetic or molecular criteria), primary induction failure (PIF) or relapsed with chemosensitive disease; SD may be included if no mass > 3 cm

Acute myeloid leukemia (AML) with any of the following:\r\n* In first remission (CR1) with intermediate risk or high-risk cytogenetic and/or molecular features\r\n* Patients in second or subsequent complete remission (CR2, CR3, etc.)\r\n* Primary refractory or relapsed AML with no more than any one of the following adverse additional features according to modified Center for International Blood and Marrow Transplant Research (CIBMTR) criteria\r\n** Duration of first CR < 6 months\r\n** Poor risk cytogenetics or molecular features (FLT-3 internal tandem duplication [ITD]; complex karyotype with >= 3 clonal abnormalities, 5q-/-5, 7q-/-7, 11q23 abnormalities, inv(3), monosomal karyotype)\r\n** Circulating peripheral blood blasts at time of enrollment\r\n** Karnofsky performance status < 90%

Acute lymphoblastic leukemia (ALL) with any of the following:\r\n* In CR1 or subsequent complete remission (CR2, CR3, etc.)\r\n* Primary refractory or relapsed ALL with no more than one of the following adverse features according to modified CIBMTR criteria\r\n** Second or subsequent relapse\r\n** Bone marrow blasts > 25% at time of enrollment\r\n** Age > 40 years

Considered at high risk for relapse as defined by:\r\n* The presence of >= 1 of the following: failure to achieve complete response (CR) post initial treatment; relapsed disease with an initial remission duration of < 12 months; or extranodal involvement at the start of pre-transplant salvage therapy

MDS – may have achieved CR through either hypomethylating agent therapy, induction chemotherapy, or other therapy

Mantle-cell NHL - may be treated in first complete remission (CR); (diagnostic lumbar puncture [LP] required pre-transplant)

Acute lymphoblastic leukemia (ALL) second or greater complete remission (CR); first complete remission (CR1) unable to tolerate consolidation chemotherapy due to chemotherapy-related toxicities; CR1 high-risk ALL; high risk ALL is defined as having one of the following:\r\n* Evidence of high risk cytogenetics such as t(9;22), t(1;19), t(4;11), other MLL rearrangements, IKZF1\r\n* 30 years of age or older at diagnosis\r\n* White blood cell counts of greater than 30,000/mcL (B-ALL) or greater than 100,000/mcL (T-ALL) at diagnosis\r\n* Central nervous system (CNS) leukemia involvement during the course of disease\r\n* Slow cytologic response (> 10% lymphoblasts in bone marrow on day 14 of induction therapy)\r\n* Evidence of persistent immunophenotypic or molecular minimal residual disease (MRD) at the end of induction and consolidation therapy

Acute myelogenous leukemia (AML) and related precursor neoplasms: 2nd or greater complete remission (CR); first complete remission (CR1) in patients > 60 years old; CR1 in =< 60 years old that is NOT considered as favorable-risk; favorable risk is defined as having one of the following:\r\n* t(8,21) without cKIT mutation\r\n* inv(16) or t(16;16) without cKIT mutation\r\n* Normal karyotype with mutated NPM1 and wild type FLT-ITD\r\n* Normal karyotype with double mutated CEBPA\r\n* Acute prolymphocytic leukemia (APL) in first molecular remission at end of consolidation

Biphenotypic/undifferentiated/prolymphocytic leukemias in first or subsequent CR, adult T-cell leukemia/lymphoma in first or subsequent CR

Burkitt’s lymphoma in second complete remission (CR2) or subsequent CR

Acute myeloid leukemia (AML) in first remission with high-risk features or in second or higher remission

Acute lymphoblastic leukemia (ALL) in first remission with high-risk features or in second or higher remission

Diagnosis of acute leukemia (AML/ALL) or advanced MDS (intermediate-2 [INT-2] or high risk) in complete remission (complete remission [CR]/composite complete remission [CRc]/complete remission with incomplete hematologic recovery [CRi]) documented by bone marrow biopsy done within 30 days prior to the initiation of conditioning regimen

Failure to achieve any objective response (CR - complete remission, PR - partial remissino, mCR - marrow complete remission, or HI - hematologic improvement), but no evidence of disease progression within the 8 weeks leading to the subject's first dose of IP (INVESTIGATIONAL PRODUCT) in this study (Cycle 1, Day 1)

Prior or ongoing response (IWG 2006: HI, PR, CR, or marrow CR) to treatment with azacitidine for injection or decitabine, at any time in the subject's prior history, which includes relapsed disease

Any patient, regardless of age or sex, with EBV-positive Hodgkin’s or non-Hodgkin’s Lymphoma, or lymphoepithelioma/leiomyosarcoma regardless of the histological subtype or EBV (associated)-T/NK-lymphoproliferative disease or severe chronic EBV \r\n* In second or subsequent relapse (or first relapse or with active disease if immunosuppressive chemotherapy contraindicated or multiply relapsed patients in remission who have a high risk of relapse) OR any patient with primary disease or in first remission if immunosuppressive chemotherapy is contraindicated, e.g. patients who develop Hodgkin disease after solid organ transplantation or if the Lymphoma is a second malignancy e.g. a Richters transformation of chronic lymphocytic leukemia (CLL) (Group A) OR\r\n* In remission or with minimal residual disease status after autologous or syngeneic stem cell transplantation (SCT) (Group B) OR\r\n* In remission or with detectable disease after allogeneic SCT (Group C)

Participants must have pathologically confirmed acute myeloid leukemia (AML) in first complete remission (CR1) as defined by:\r\n* Bone marrow biopsy with < 5% blasts\r\n* No clusters or collections of blast cells\r\n* No extramedullary leukemia\r\n* Absolute neutrophil count >= 1000/uL (achieved post-induction at some point)\r\n* Please note that full platelet recovery is not necessary, and thus, patients achieving pathological complete remission (CRp) are eligible

Creatinine (Cr) > 2.0

Creatinine (Cr) =< 1.5

Patients who have achieved complete remission of intestinal metaplasia (CR-IM)

Tumor tissue or blood collections from patients with benign tumors including but not limited to desmoid tumors, carcinoma in situ, or ongoing complete disease response (CR)

In remission (complete remission [CR], partial remission [PR], or stable disease based on clinical, not necessarily radiologic, assessment) and currently being observed and with no current cytotoxic chemotherapy planned; patients may be on rituximab maintenance

Documentation of target and non-target lesion(s) status per RECIST1.1 post induction chemotherapy for patients with evaluable disease\r\n* Note: Evaluable disease is not required for study entry (patients with complete response [CR] or response sufficient to preclude measurable lesions are not excluded; such patients will be evaluated for PFS and OS, but not for response)

Has relapsed (disease progression after most recent therapy) or refractory (failure to achieve Complete Response [CR] or Partial Response [PR] to most recent therapy) classical Hodgkin Lymphoma.