Known central nervous system (CNS) lymphoma Medically apparent central nervous system lymphoma or leptomeningeal disease Central nervous system lymphoma or leptomeningeal infiltration History of central nervous system lymphoma (either primary or metastatic). Central nervous system (CNS) lymphoma or leptomeningeal infiltration Known central nervous system lymphoma. Known central nervous system (CNS) lymphoma Current central nervous system (CNS) lymphoma or leptomeningeal infiltration. Known central nervous system (CNS) lymphoma Known central nervous system (CNS) lymphoma Known central nervous system lymphoma Known central nervous system (CNS) lymphoma Presence of central nervous system (CNS) lymphoma Patients with active known central nervous system (CNS) involvement of CLL or lymphoma; (patients with history of CNS CLL or lymphoma now in remission are eligible for the trial) Diagnosis of primary central nervous system lymphoma Prior therapy for central nervous system (CNS) lymphoma\r\n* Steroids not an exclusion Known central nervous system (CNS) lymphoma or leukemia Known central nervous system (CNS) lymphoma History of central nervous system lymphoma (either primary or metastatic). Central nervous system lymphoma, including lymphomatous meningitis Patients with active and/or untreated central nervous system (CNS) lymphoma will not be eligible History of central nervous system lymphoma (either primary or metastatic). Primary central nervous system (CNS) lymphoma Has known active central nervous system (CNS) lymphoma Has known active central nervous system (CNS) lymphoma Known central nervous system (CNS) lymphoma Central nervous system (CNS) or meningeal involvement, or cord compression by the lymphoma; history of CNS lymphoma Known central nervous system lymphoma Central nervous system (CNS) lymphoma Known active central nervous system lymphoma Active central nervous system lymphoma All patients with central nervous system lymphoma Central nervous system (CNS) lymphoma: CNS involvement by lymphoma, including parenchymal brain or spinal cord lymphoma or known presence of leptomeningeal disease prior to registration Patients with evidence of active central nervous system lymphoma Known central nervous system lymphoma Known central nervous system (CNS) lymphoma Active central nervous system (CNS) disease defined as symptomatic meningeal lymphoma or known CNS parenchymal lymphoma; a lumbar puncture demonstrating DLBCL at the time of registration to this study is not exclusion for study enrollment Active central nervous system lymphoma Known active central nervous system or leptomeningeal lymphoma Known history of, or clinically apparent, central nervous system (CNS) lymphoma or leptomeningeal lymphoma. Primary central nervous system (CNS) lymphoma Known central nervous system (CNS) lymphoma or leukemia Patients should not have evidence of active central nervous system lymphoma All patients with central nervous system lymphoma. Lymphoma involving the central nervous system Central nervous system (CNS) involvement by lymphoma including parenchymal brain or spinal cord lymphoma or known presence of leptomeningeal disease prior to registration Lymphoma involving the central nervous system Known active central nervous system or leptomeningeal lymphoma Current or past history of central nervous system lymphoma Patients with primary central nervous system (CNS) lymphoma Central nervous system lymphoma or leptomeningeal infiltration Known central nervous system lymphoma Known active central nervous system lymphoma or leptomeningeal disease Central nervous system lymphoma or leptomeningeal infiltration Participants with central nervous system (CNS) lymphoma Lymphoma involving the central nervous system Known central nervous system lymphoma (either primary or metastatic). Patients with active central nervous system (CNS) disease defined as symptomatic meningeal lymphoma or known CNS parenchymal lymphoma Known central nervous system (CNS) lymphoma Known central nervous system lymphoma or leptomeningeal disease, except subjects with a history of central nervous system lymphoma treated and in remission > 6 months Known central nervous system (CNS) lymphoma All patients with central nervous system lymphoma Known central nervous system lymphoma Known central nervous system (CNS) lymphoma Known central nervous system lymphoma Known central nervous system or primary mediastinal lymphoma All patients with history of central nervous system lymphoma Known active Central Nervous System (CNS) lymphoma. No active central nervous system (CNS) disease defined as symptomatic meningeal lymphoma or known CNS parenchymal lymphoma; a lumbar puncture demonstrating mantle cell lymphoma at the time of registration to this study is not an exclusion for study enrollment Primary central nervous system (CNS) lymphoma History of central nervous system lymphoma (either primary or metastatic) or leptomeningeal disease. Medically apparent central nervous system lymphoma or leptomeningeal disease Central nervous system lymphoma or leptomeningeal disease Active central nervous system (CNS) lymphoma Known central nervous system lymphoma History of lymphoma involving the central nervous system Known central nervous system (CNS) lymphoma Central nervous system (CNS) lymphoma All patients with active central nervous system lymphoma Clinical evidence of extra-central nervous system (CNS) (systemic) non-Hodgkin lymphoma Central Nervous System (CNS) Lymphoma or chronic immunosuppression-associated central nervous system (CNS) lymphoma. Medically apparent central nervous system lymphoma or leptomeningeal disease Primary central nervous system (CNS) lymphoma Central nervous system or leptomeningeal lymphoma Primary central nervous system (CNS) lymphoma Evidence of central nervous system lymphoma or lymphomatous meningitis Patients with active central nervous system (CNS) lymphoma Central nervous system (CNS) metastases from lymphoma or small cell lung cancer Known central nervous system (CNS) lymphoma, leptomeningeal lymphoma Known central nervous system lymphoma Central nervous system (CNS) lymphoma; active brain or leptomeningeal metastases. Diagnosis of primary central nervous system (CNS) lymphoma Known central nervous system (CNS) lymphoma Known central nervous system (CNS) lymphoma Patients with central nervous system (CNS) lymphoma are not eligible for the trial unless the disease had been treated and the subject remains without symptoms with no active CNS lymphoma. Have known central nervous system metastasis or Central Nervous System lymphoma; History or current evidence of central nervous system lymphoma History of primary central nervous system lymphoma or neoplastic central nervous system disease Known central nervous system (CNS) lymphoma or leukemia Known central nervous system involvement by PTCL Patients with evidence of current central nervous system leukemic involvement Central nervous system involvement Presence of active/uncontrolled central nervous system involvement Patients with any central nervous system involvement or CTCL. Central nervous system involvement Central nervous system involvement by lymphoma, including leptomeningeal involvement EXCLUSION - INFUSION: Patients with central nervous system involvement Myeloma-related central nervous system involvement Central nervous system involvement Central nervous system involvement with lymphoma at any time in the patient’s history; intrathecal prophylaxis during induction is allowed as long as active disease has not been identified Suggestive central nervous system involvement with leukemia Central nervous system involvement Symptomatic central nervous system involvement. Central nervous system involvement. Known central nervous system or meningeal involvement (in the absence of symptoms investigation into central nervous system involvement is not required) Evidence of lymphoma outside of the central nervous system\r\n* Ocular involvement will not exclude Known central nervous system involvement Known active involvement of the central nervous system by lymphoma or leukemia Subjects are not eligible if there is a prior history or current evidence of central nervous system or leptomeningeal involvement Has either clinical evidence of or history of central nervous system involvement by AML. Active or previous central nervous system leukemia involvement Patients who have known central nervous system involvement with multiple myeloma will be excluded from this clinical trial Active or previous central nervous system leukemia involvement Central nervous system involvement with MM (by clinical symptoms and signs). Active involvement of the central nervous system with malignancy No known history or suspicion of central nervous system involvement by lymphoma Central nervous system metastases, including leptomeningeal involvement Known central nervous system involvement with the disease under study Primary central nervous system involvement only Patients with known central nervous system involvement should be excluded from this clinical trial Has known active central nervous system involvement of the malignancy. Patients with known or suspected central nervous system involvement of lymphoma. All patients with central nervous system involvement with lymphoma Known lymphomatous involvement of the central nervous system History of central nervous system multiple myeloma involvement Subjects with known central nervous system involvement with multiple myeloma Active involvement of the central nervous system with malignancy Known active central nervous system involvement Central nervous system involvement of the disease under study Central nervous system involvement Known lymphomatous involvement of the central nervous system Known central nervous system involvement Presence of central nervous system involvement of leukemia or a history of primary central nervous system leukemia. Patients must not have active central nervous system involvement Primary central nervous system lymphoma or known intracranial involvement Subjects are not eligible if there is a prior history or current evidence of central nervous system or leptomeningeal involvement Known central nervous system or meningeal involvement (in the absence of symptoms, investigation into central nervous system involvement is not required) Active involvement of the central nervous system with malignancy Active involvement of the central nervous system with malignancy Central nervous system involvement. Active central nervous system involvement with AML. Known central nervous system or meningeal involvement (in the absence of symptoms, investigation into central nervous system involvement is not required) Known active involvement of the central nervous system by lymphoma or leukemia Known central nervous system involvement by multiple myeloma Patients with known central nervous system involvement should be excluded from this clinical trial Central nervous system involvement (Bing-Neel syndrome) Known involvement of central nervous system Central nervous system involvement by lymphoma, including leptomeningeal involvement Clinical evidence of central nervous system involvement. Known central nervous system involvement or brain metastases Active central nervous system involvement by leukemia Active central nervous system involvement Patients with a history of central nervous system involvement by CLL or who have prolymphocytic leukemia (PLL) Patients with documented central nervous system involvement of AML Active central nervous system involvement by malignancy Documented current central nervous system involvement by multiple myeloma History of or current, central nervous system involvement with AML. Known clinically active central nervous system involvement. Subject has known active central nervous system involvement with AML. Patients with controlled asymptomatic central nervous system involvement are allowed. Central nervous system involvement with lymphoma, including parenchymal and leptomeningeal disease Subjects with Central Nervous System involvement with multiple myeloma Central nervous system involvement of the CLL Active uncontrolled central nervous system involvement Presence or history of central nervous system involvement by lymphoma. Patients with known central nervous system involvement at the time of study entry will be excluded from this clinical trial Primary or secondary Central Nervous System involvement by lymphoma. Myeloma-related central nervous system involvement Patients with leukemic involvement of the central nervous system Central nervous system involvement (based on clinical assessment) Known clinically active central nervous system involvement Known active involvement of the central nervous system by lymphoma or leukemia Central nervous system involvement Known lymphomatous involvement of the central nervous system. Known central nervous system or meningeal involvement (in the absence of symptoms investigation into central nervous system involvement is not required) Active central nervous system involvement by lymphoma Known central nervous system involvement Central nervous system involvement. Known involvement of the central nervous system by WM. Central nervous system involvement Patients with a history of central nervous system involvement by lymphoma Active involvement of the central nervous system with malignancy Central nervous system disease involvement Central nervous system involvement Known Central nervous system involvement, brain metastasis Known central nervous system or meningeal involvement (in the absence of symptoms investigation into central nervous system involvement is not required); patients with human T-cell lymphotropic virus type 1 (HTLV1) adult T-cell leukemia/lymphoma (ATLL) and controlled central nervous system (CNS) or meningeal involvement may be enrolled after discussion with the Memorial Sloan Kettering (MSK) principal investigator Known active central nervous system involvement Central nervous system involvement. Presence or history of central nervous system involvement by lymphoma Known central nervous system involvement by leukemia No known central nervous system involvement by myeloma. Disease-related central nervous system involvement Documented current central nervous system involvement by leukemia or lymphoma CLL central nervous system involvement No known involvement of central nervous system by lymphoma Evidence of sanctuary site involvement by disease, e.g., central nervous system, ocular, testicular involvement Active involvement of the central nervous system with malignancy Untreated central nervous system involvement Known central nervous system involvement Known central nervous system involvement Active central nervous system involvement by malignancy; central nervous system disease that has been treated into remission is permitted; a chart note of the clinician’s impression of lack of central nervous system (CNS) involvement is acceptable Documented current central nervous system involvement Symptomatic central nervous system involvement Known uncontrolled central nervous system involvement Lymphoma involvement of the central nervous system For Part B only: Known leukemic involvement or clinical symptoms of leukemic involvement of the central nervous system Central nervous system involvement Patients with a history of central nervous system involvement by lymphoma Patients with known central nervous system involvement. Known, active (symptomatic) involvement of the central nervous system by leukemia. Known leukemic involvement of the central nervous system. Documented current central nervous system involvement by leukemia or lymphoma Central nervous system involvement Has central nervous system involvement History of central nervous system involvement of lymphoma; All patients with active central nervous system involvement with lymphoma INCLUSION CRITERIA FOR PATIENTS: No central nervous system involvement of disease Patients with active central nervous system involvement Symptomatic central nervous system involvement. History of central nervous system involvement or symptoms suggestive of central nervous system involvement by multiple myeloma Known central nervous system involvement by multiple myeloma Known uncontrolled central nervous system involvement by malignant disease Patients must have histologically or cytologically confirmed relapsed/refractory CD30 low (< 10%) TCL:\r\n* Peripheral TCL not otherwise specified (PTCL NOS)\r\n* Angioimmunoblastic T cell lymphoma (AITL)\r\n* Hepato-splenic T cell lymphoma (HTCL)\r\n* Adult T cell leukemia/lymphoma (ATLL)\r\n* Enteropathy associated T cell lymphoma (EATL)\r\n* Natural killer (NK) T cell lymphoma (NK/TCL)\r\n* Transformed mycosis fungoides Patients must have histologically confirmed mantle cell lymphoma (MCL)\r\n* Please note: measurable disease is not required, but will be followed if it exists Histologic diagnosis other than a mature B-cell lymphoma as defined in the WHO classification Peripheral T-cell lymphoma-not otherwise specified (PTCL-NOS); Natural-killer/T-cell lymphoma (NKTL) Relapsed or refractory mantle cell lymphoma (MCL) with no adequate therapies. Biopsy proven plasmablastic lymphomas, or peripheral T cell lymphoma (with the exception of anaplastic lymphoma kinase positive [ALK+] type in first or second complete remission) (timeline 8 months prior to enrollment) Cutaneous T cell Lymphoma (CTCL) NHL SA expansion: Mature B-cell NHL with the following histologies: primary mediastinal lymphoma, DLBCL, and B-cell lymphoma not specified that is R/R to standard therapy and for whom standard treatments are contraindicated or unavailable Angioimmunoblastic T-cell lymphoma (AITL) Enteropathy-associated T-cell lymphoma Extranodal natural killer (NK) T-cell lymphoma, nasal type Hepatosplenic T-cell lymphoma Peripheral T-cell lymphoma, no otherwise specified (NOS) Precursor T-cell lymphoma or leukemia Adult T-cell lymphoma/leukemia (ATLL) Histologically confirmed diagnosis of PTCL (using the most recent edition of the World Health Organization [WHO] Classification of Tumors of Hematopoietic and Lymphoid Tissues as guidance) including: \r\n* Anaplastic large cell lymphoma, anaplastic large cell kinase (ALK)-negative \r\n* Angioimmunoblastic T-cell lymphoma \r\n* Enteropathy-type T-cell lymphoma\r\n* Hepatosplenic gamma-delta T-cell lymphoma \r\n* Peripheral T-cell lymphoma, unspecified (not otherwise specified [NOS]) \r\n* Transformed mycosis fungoides\r\n* Subcutaneous panniculitis-like T-cell lymphoma. \r\n* NOTE: patients with adequate archived (well-preserved, formalin-fixed) biopsy tissue remaining will be required to submit a portion for exploratory studies; this is not optional if tissue is available; however, lack of adequate tissue for exploratory studies will not preclude patients from participating Patients with a diagnosis of any of the following are not eligible:\r\n* Anaplastic large cell lymphoma, ALK-positive \r\n* Adult T-cell lymphoma/leukemia (ATLL)\r\n* Anaplastic large-cell lymphoma, primary cutaneous type\r\n* Precursor T-lymphoblastic lymphoma/leukemia\r\n* Mycosis fungoides/Sezary syndrome (except transformed mycosis fungoides [MF])\r\n* Natural killer (NK)-cell leukemia\r\n* T-cell granular lymphocytic leukemia\r\n* T-cell prolymphocytic leukemia Patients with T-cell or B cell lymphoblastic lymphoma confirmed by conventional immature T- or pre B cell markers even if the bone marrow is not involved are also eligible 3. High Grade B-cell Lymphoma---Burkitt's like. Patients with newly diagnosed Group A (low risk) lymphoma. Patients with Group B (intermediate risk) if classified as Murphy Stage III/IV and diagnostic LDH > 2 XULN and patients with primary mediastinal B-cell lymphoma (PMBL). PROCUREMENT: Diagnosis of Hodgkin’s or non-Hodgkin’s lymphoma:\r\n* GROUP A: \r\n** With active disease \r\n*** In second or subsequent relapse\r\n*** In first relapse for indolent lymphoma after first line therapy for relapse\r\n*** Or first relapse if immunosuppressive chemotherapy contraindicated\r\n*** Primary refractory disease or if persistent disease after first line therapy of relapse\r\n** Or multiply relapsed patients in remission who are at a high risk of relapse or the lymphoma is a second malignancy e.g. a Richter's transformation of chronic lymphocytic leukemia (CLL) after failing frontline therapy OR\r\n* GROUP B:\r\n** After autologous or syngeneic stem cell transplant (SCT) (as adjuvant therapy) B-CLL or recurrent or refractory B-cell lymphoma (or other B-cell neoplasm) or multiple myeloma monoclonal for Kappa-light chain Prior therapy must include a BTK inhibitor in diseases for which approved therapy includes a BTK inhibitor (i.e., SLL/CLL, WM, and mantle cell lymphoma). Subjects with DLBCL must have failed, refused, or be ineligible for autologous stem cell transplant. Subjects with low grade lymphoma must be progressing and requiring treatment. Falls under one of the following subtypes of CD52 positive non-Hodgkin lymphoma (defined as >= 50% positive staining by immunohistochemical staining or flow cytometry by local lab):\r\n* High-grade B-cell lymphoma, with MYC and BCL2 and/or BCL6 rearrangements (DHL)\r\n* DLBCL or high-grade B-cell lymphoma NOS or B-cell lymphoma unclassifiable with features intermediate between Burkitt lymphoma and diffuse large B-cell lymphoma with MYC and BCL2 protein over-expression by immunohistochemical (IHC) staining as defined by MYC expression in >= 30% of cells and BCL2 positivity >= 50% (DOL)\r\n* Transformed lymphoma with MYC rearrangement by fluorescence in situ hybridization (FISH) or over-expression by IHC, as above\r\n* CD52 positive mature T-cell lymphoproliferative disorder Histologically confirmed mature peripheral T-cell or natural killer (NK)-cell lymphoma per World Health Organization (WHO) classification, including: \r\n* Anaplastic lymphoma kinase (ALK)-positive anaplastic large cell lymphoma (ALCL) with international protein index (IPI) of 2 or higher (must have stage III-IV disease)\r\n* ALK-negative ALCL\r\n* PTCL-not otherwise specified (NOS)\r\n* Angioimmunoblastic T-cell lymphoma (AITL)\r\n* Adult T-cell lymphoma/leukemia (ATLL) \r\n* Enteropathy-associated T-cell lymphoma (EATL)\r\n* Hepatosplenic T-cell lymphoma INCLUSION - PROCUREMENT: Referred patients will initially be consented for procurement of blood for generation of the transduced ATL; eligibility criteria at this stage include:\r\n* Diagnosis of recurrent T-cell acute lymphoblastic leukemia (T-ALL), T-cell acute lymphoblastic lymphoma (T-LLy), or T-non-Hodgkin lymphoma (T-NHL, including angioimmunoblastic T-cell lymphoma [AITL], enteropathy-associated T-cell lymphoma [EATL], monomorphic epitheliotropic intestinal T-cell lymphoma [MEITL], peripheral T-cell lymphoma [PTCL] not otherwise specified [NOS], anaplastic large cell lymphoma [ALCL] adult T-cell leukemia/lymphoma, T cell prolymphocytic leukemia with symptomatic disease, extranodal natural killer [NK]/T cell lymphoma, mycosis fungoides/ Sezary syndrome stage IIb or higher)\r\nAND\r\n* suitable for allogeneic hematopoietic stem cell transplant (HSCT)\r\n** with confirmation of an identified eligible allogeneic (allo)-HSCT donor by a Foundation for the Accreditation of Cellular Therapy (FACT) accredited transplant center AND \r\n** with confirmation that the center plans to proceed with transplant if CD5.CAR treatment induces a complete remission\r\n* For T-NHL subjects, eligibility will be confined to disease stages where allogeneic HSCT is indicated INCLUSION - TREATMENT: Diagnosis of recurrent T-cell acute lymphoblastic leukemia (T-ALL), T-cell acute lymphoblastic lymphoma (T-LLy), or T-non-Hodgkin lymphoma (T-NHL, including angioimmunoblastic T-cell lymphoma [AITL], enteropathy-associated T-cell lymphoma [EATL], monomorphic epitheliotropic intestinal T-cell lymphoma [MEITL], peripheral T-cell lymphoma [PTCL] NOS, anaplastic large cell lymphoma [ALCL], adult T-cell leukemia/lymphoma, T cell prolymphocytic leukemia with symptomatic disease, extranodal NK/T cell lymphoma, mycosis fungoides/ Sezary syndrome stage IIB or higher) AND\r\n* suitable for allogeneic hematopoietic stem cell transplant (HSCT) \r\n** with confirmation of an identified eligible allo-HSCT donor by a FACT accredited transplant center AND\r\n** with confirmation that the center plans to proceed with transplant if CD5.CAR treatment induces a complete remission\r\n* For T-NHL subjects, eligibility will be confined to disease stages where allogeneic HSCT is indicated INCLUSION - PROCUREMENT: Any patient, regardless of age or sex, with measurable EBV-positive Hodgkin’s or non-Hodgkin’s lymphoma, (regardless of the histological subtype) or EBV (associated)-T/natural killer (NK)- or B cell lymphoproliferative disease\r\n* The first 3 patients enrolled will be adults; patients <18 years of age are eligible if those first 3 patients do not experience dose limiting toxicity considered to be primarily related to the EBVST or nivolumab\r\n* Patients with relapsed or refractory lymphoma who failed or are ineligible for an autologous hematopoietic cell transplantation are also eligible for this study Key Inclusion Criteria:\n\n -Any of the following as defined by the WHO, 2016 lymphoid neoplasm classifications and\n histologically confirmed:\n\n - Diffuse large B-cell lymphoma (DLBCL), Not Otherwise Specified (NOS): Germinal center\n B-cell type (GCB), Activated B-cell type (ABC)\n\n - High-grade B-cell lymphoma (HGBCL) NOS\n\n - HGBCL with MYC and BCL2 and/or BCL6 rearrangements\n\n - T-cell histocyte-rich large B-cell lymphoma\n\n - EBV+ DLBCL, NOS\n\n - HHV8+ DLBCL, NOS\n\n Relapsed or refractory disease following at least 2 lines (and a maximum of 4 lines) of\n prior rituximab containing multi-agent chemotherapy which may include an autologous stem\n cell transplantation unless patients are not considered suitable for intensive second-line\n chemotherapy or autologous stem cell transplantation. Patients who are ineligible for\n intensive second line chemotherapy,must have received at least one prior\n rituximab-containing combination chemotherapy regimen. Patients who are ineligible for\n intensive second line chemotherapy, must have received at least one prior\n rituximab-containing combination chemotherapy regimen.\n\n - Baseline measurable disease with at least 1 bi dimensional lesion with longest\n diameter (LDi) >1.5cm on CT scan which is FDG avid on PET scan.\n\n - A biopsy (archived or Screening/recent) will be collected at Screening.\n\n - At least 18years of age (or ?20 years in Japan).\n\n - Eastern Cooperative Oncology Group (ECOG) Performance Status (PS) 0 or 1.\n\n Key Exclusion Criteria:\n\n - Active central nervous system (CNS) lymphoma.\n\n - Prior organ transplantation including prior allogeneic SCT.\n\n - Prior therapy with an anti PD 1, anti PD L1, anti PD L2, anti CD137, or anti cytotoxic\n T lymphocyte associated antigen 4 (CTLA 4) antibody (including ipilimumab,\n tremelimumab or any other antibody, or drug specifically targeting T cell co\n stimulatory or immune checkpoint pathways). Mantle cell lymphoma Any histologies not specifically mentioned must be discussed with medical monitor.For subjects enrolled in the phase 3 portion of study, pathologic samples will be submitted for central confirmation of disease histology. Pathology confirmed relapsed or refractory T-cell lymphoma (PTCL and stage > IB CTCL) at treating institution Patients with mature B-cell ALL will be removed from the protocol as soon as that diagnosis is made and should be treated on a B-cell leukemia (Burkitt’s) protocol; NOTE: patients with T-cell surface markers and a t(8;14)(q24;q11) remain eligible Patients with systemic T cell lymphoma of any stage and any subtypes; patient must have had at least one standard chemotherapy and measurable disease at the time of enrollment Patients must have relapsed (first or greater relapse) or refractory lymphoma with:\r\n* Lymphoblastic lymphoma or peripheral T-cell lymphoma\r\n* Histologic verification of disease at original diagnosis or subsequent relapse\r\n* Evaluable or measurable disease documented by clinical or radiographic criteria or bone marrow disease present at study entry\r\n* Patient may have CNS 2 status if other sites of leukemia or lymphoma involvement are present Histologically confirmed mantle cell lymphoma (confirmation of cyclin D1 positivity on diagnostic biopsy) Subjects with ALK+, anaplastic large cell lymphoma (ALCL) should have been treated with, be ineligible for, or have refuse chemotherapy and brentuximab prior to enrollment on the current study. 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 Relapsed or refractory T-cell lymphoma (TCL) biopsy-proven =< 6 months prior to registration, including the following subtypes:\r\n* Peripheral T-cell lymphoma, not otherwise specified\r\n* Anaplastic large cell lymphoma, anaplastic lymphoma kinase (ALK) negative, primary systemic type\r\n* Angioimmunoblastic T-cell lymphoma\r\n* Extranodal natural killer (NK)/T-cell lymphoma, nasal type\r\n* Adult T-cell lymphoma/leukemia (human T-lymphotropic virus 1 [HTLV1]+)\r\n* Blastic NK-cell lymphoma\r\n* Enteropathy-associated T-cell lymphoma\r\n* Hepatosplenic gamma delta T-cell lymphoma\r\n* Transformed mycosis fungoides\r\n* T/NK-cell lymphoma, unclassifiable Eligible patients with Hodgkin lymphoma must fulfill one of the following criteria: 1) have received two prior therapies, one of which must be an autologous stem cell transplant, or 2) have received three prior lines of therapy; eligible patients with any of the listed peripheral T cell lymphomas or non-Hodgkin lymphomas must have received two lines of prior therapy, at least one of which must contain cytotoxic chemotherapy; patients with diffuse large B-cell lymphoma or primary mediastinal B-cell lymphoma must have received 2 prior treatment regimens at least 1 of which included an anthracycline and an anti-CD20 monoclonal antibody Relapsed or refractory:\r\n* Multiple myeloma (MM) previously treated with an immunomodulatory drug (IMID), a proteosome inhibitor and an alkylating agent; OR\r\n* Acute myeloid leukemia (AML), excluding acute promyelocytic leukemia (PML-RARA rearranged- AML-M3); either primary refractory or relapsed/refractory disease after at least two front line chemotherapy regimens (note: induction and consolidation chemotherapy is considered one line of therapy); diagnosis based on 2008 World Health Organization (WHO) criteria; OR\r\n* Relapsed T-cell lymphoma (TCL) or the following types: peripheral T-cell lymphoma-not otherwise specified (PTCL-NOS); angioimmunoblastic T-cell lymphoma (AITL), anaplastic large cell (ALCL), and cutaneous TCL (CTCL) of mycosis fungoides (MF); patients should have failed standard therapy and in the case of PTCL-NOS, AITL, and ALCL either have failed or be ineligible for high-dose therapy with autologous stem cell transplant CUTANEOUS T-CELL LYMPHOMA (CTCL) ONLY PERIPHERAL T-CELL LYMPHOMA (PTCL) ONLY Large cell lymphoma, mantle cell lymphoma and Hodgkin disease that is progressing on salvage therapy Mantle cell lymphoma ([MCL] with the exception of aggressive MCL, defined as Ki67 > 30%, or blastoid histology) Primary disease of hematologic origin, lymphoma, or small cell cancer Phase I or II patients who have received prior dose-adjusted EPOCH for treatment for PEL or KSHV-associated large cell lymphoma Primary lesions with the following histologies: small cell carcinoma, germ-cell tumors, lymphoma, leukemia, and multiple myeloma Histologically or cytologically-proven T- or B-cell lymphoma Treatment with alemtuzumab or other T cell-depleting antibodies within 6 months of T cell therapy All subjects must have a diagnosis of ALL of either B-cell, T-cell, or mixed (i.e., B/T lineage) Large cell lymphoma, mantle cell lymphoma and Hodgkin disease that is progressing on salvage therapy Mantle cell lymphoma patients who are beyond first remission and previously treated with chemoimmunotherapy; patients who have relapsed following autologous hematopoietic cell transplant (HCT) are eligible Patients diagnosed with a leukemia or lymphoma as follows:\r\n* Chronic or acute leukemia forms of HTLV-1 associated adult T-cell leukemia;\r\n* Peripheral T-cell lymphoma (angioimmunoblastic, hepatosplenic, or not otherwise specified); or,\r\n* Cutaneous T-cell lymphoma stage III or IV with circulating monoclonal cells (B1 or B2) and/or erythrodermia (T4)\r\n* T-cell prolymphocytic leukemia (T-PLL)\r\n* NOTE: Diagnosis must be validated by the Pathology Department, National Cancer Institute (NCI) Patients must have been refractory or relapsed following front line therapy for adult T-cell leukemia (ATL); those with cutaneous T-cell lymphoma (CTCL) or peripheral T-cell lymphoma (PTCL) who have CD30+ disease must have progressed during or after treatment with brentuximab vedotin, or are unable to receive treatment due to allergy or intolerance Diagnosis of either cutaneous T-cell lymphoma; T-prolymphocytic leukemia; T-large granulocytic leukemia; T-lymphoblastic leukemia/lymphoma; or peripheral T-cell lymphoma, natural killer/T-cell lymphoma for whom allogeneic stem cell transplantation is indicated Participants with primary mediastinal B-cell lymphoma (PMBCL) Pathologic diagnosis of one of the following:\r\n* For dose escalation:\r\n** Confirmed diagnosis of peripheral T-cell lymphoma (PTCL) or angioimmunoblastic T-cell lymphoma (AITL) that is refractory to at least one line of therapy; anaplastic large cell lymphoma (ALCL) and natural killer T-cell lymphoma nasal type (NKTCL) are excluded\r\n** Advanced stage cutaneous T-cell lymphoma (CTCL), specifically CTCL NOS, small/medium T-cell lymphoma (SMTCL) and mycosis fungoides (MF) stage IB, IIA, IIB, III and IV that have relapsed after at least one specific prior therapy (e.g. interferon, photopheresis, denileukin difitox, bexarotene, etc); anaplastic cutaneous large cell lymphoma (ACLCL) and lymphomatoid papulopsis are excluded\r\n** Follicular lymphoma grade 1, 2 or 3A that meets the following criteria: \r\n*** Relapsed or refractory to at least 2 lines of therapy AND\r\n*** Relapsed or refractory post autologous cell transplantation (HCT)\r\n* For dose expansion/dose confirmation phase: \r\n** Patients with confirmed diagnosis of peripheral T-cell lymphoma (PTCL) follicular type or angioimmunoblastic T-cell lymphoma (AITL) that is refractory to at least one line of therapy Patients must have histologically confirmed relapsed/refractory or previously untreated mantle cell lymphoma (any stage) Primary lesion with radiosensitive histology that includes the following: small cell carcinoma, germ cell tumors, lymphoma, leukemia, or multiple myeloma 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 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 STEP 1: Within 30 days of study entry: T cell leukemia or lymphoma COH pathology review confirms that research participant’s diagnostic material is consistent with recurrent/progressive/residual B cell lymphoproliferative neoplasms as listed below AND the research participant is not eligible for or declines COH IRB Protocol No. 13277; additionally, CD19 positivity must be documented in a pathology report if the research participant previously received CD19-targeted therapy; however, it is not a requirement that the CD19 testing be performed by a COH pathologist\r\n* Disease stratum 1 (NHL): Unclassifiable high grade lymphoma, mantle cell lymphoma, follicular lymphoma, diffuse large B-cell lymphoma (DLBCL) and all its subtypes, Burkitt lymphoma (BL), marginal zone B-cell lymphoma, hairy cell leukemia, lymphoplasmacytic lymphoma, B cell lymphoma unclassifiable with features intermediate between DLBCL and BL, B cell lymphoma unclassifiable with features intermediate between DLBCL and classical Hodgkin lymphoma, and those research participants who either declined or were not eligible for COH IRB Protocol No. 13277, or who collected autologous T cells for COH IRB Protocol No. 13277 but then became ineligible for autologous hematopoietic stem cell transplant (HSCT) or participants who have relapsed following prior T cell therapy on either COH IRB Protocol No. 09174 or 12224 may be enrolled on this study\r\n* Disease stratum 2 (CLL/PLL/SLL): chronic lymphocytic leukemia (CLL), and B-cell prolymphocytic leukemia (PLL), and small lymphocytic lymphoma (SLL) Patients must have histologic or cytologic diagnosis of hematologic malignancies with an indication for allogeneic hematopoietic progenitor cell transplantation, who are ineligible to receive a full ablative conditioning regimen as part of their transplantation, including:\r\n* Acute myeloid leukemia (AML)\r\n** As post-remission therapy in patients with intermediate and high risk cytogenetic and molecular abnormalities, including therapy-related leukemia\r\n** Patients refractory to induction chemotherapy\r\n** Relapsed after complete remission\r\n* Acute lymphocytic leukemia (ALL)\r\n** As post remission therapy in Philadelphia chromosome positive (Ph+) and Philadelphia chromosome negative (Ph-) ALL in complete remission, with or without minimal residual disease in patients older than 55 years of age and those younger than 55 years but ineligible for treatment with fully ablative conditioning regimens\r\n** Relapsed or refractory after prior therapy\r\n* Non Hodgkin lymphoma\r\n** Aggressive lymphoma (Burkitt, diffuse large B cell lymphoma, plasmablastic lymphoma, mantle cell lymphoma) relapsed after autologous hematopoietic progenitor transplantation or patients ineligible to receive autologous hematopoietic progenitor transplantation because of mobilization failure or persistent bone marrow involvement by lymphoma\r\n** Indolent lymphoma (follicular, marginal zone lymphoma, mantle cell lymphoma, etc.) patients are eligible if they have received at least two lines of therapy and have remission of their extramedullary disease\r\n** Indolent and aggressive lymphoma patients with refractory disease to at least two lines of therapy\r\n* Hodgkin lymphoma\r\n** Patients relapsed after autologous hematopoietic progenitor transplantation with remission of at least their extramedullary disease after salvage therapy\r\n** Patients with refractory disease to at least 2 lines of chemotherapy\r\n* Multiple myeloma\r\n** Patients who have presented with relapsed or refractory disease after second line therapy\r\n* Myelodysplastic syndrome\r\n** Patients with International Prognostic Score System Risk rating of: intermediate – 2 and higher, ineligible to receive a fully ablative conditioning regimen for allogeneic hematopoietic progenitor cell transplantation\r\n* Chronic lymphocytic leukemia\r\n** Patients with disease relapsed or refractory after 2 or more lines of therapy, ineligible to receive fully ablative conditioning regimens for allogeneic hematopoietic progenitor cell transplantation\r\n** Patients with disease transformed to aggressive lymphoma (Richter transformation) who have received induction therapy for their aggressive disease\r\n* Chronic myeloid leukemia:\r\n** In chronic phase that has failed therapy with at least 3 different tyrosine kinase inhibitors or has progressed to accelerated or blast phase\r\n** In accelerated or blast crisis\r\n* Myeloproliferative syndromes including myelofibrosis\r\n* Complete remission is not necessary for enrollment in this protocol, however Hodgkin and non Hodgkin lymphoma must have had remission of all extramedullary disease to be eligible to participate in this trial Patients must have a previously documented histologic diagnosis of multiple myeloma (MM) Hodgkin’s Disease (HD) or non-Hodgkin’s lymphoma (NHL), and be eligible to undergo autologous PBSC transplantation on institutional protocols\r\n* Multiple myeloma should be in first or second partial response or better, as defined by International Myeloma Working Group criteria\r\n* Hodgkin’s Disease should be primary refractory or relapsed (either chemosensitive or refractory)\r\n* Non-Hodgkin’s lymphoma must be in either first or second partial response or better and have any one of the following histologies:\r\n** Diffuse large B cell lymphoma\r\n** Transformed lymphoma\r\n** Mantle cell lymphoma\r\n** Follicular lymphoma (any grade)\r\n** Peripheral T cell lymphoma Autologous patients can be included anytime within 6 months post-transplant, if they had no signs of progression and meet one of the following criteria: i. leukemia; ii. lymphoma (all types of B and T cell lymphoma); iii. multiple myeloma PROCUREMENT INCLUSION CRITERIA\r\n* Diagnosis of recurrent aggressive or indolent B-cell lymphoma or CLL, or newly diagnosed patients unable to receive or complete standard therapy OR diagnosis of relapsed/refractory aggressive B-cell lymphoma with a treatment plan that will include high dose therapy and autologous stem cell transplantation\r\n* CD19-positive tumor (result can be pending at this time)\r\n* Hemoglobin (Hgb) > 8.0\r\n* If pheresis required to collect blood:\r\n** Creatinine < 1.5 × upper limit normal\r\n** Aspartate aminotransferase (AST) < 1.5 × upper limit normal\r\n** Prothrombin time (PT) and activated partial thromboplastin time (APTT) < 1.5 × upper limit normal\r\n* Informed consent explained to, understood by and signed by patient/guardian (and donor, where applicable); patient/guardian given copy of informed consent Diagnosis of recurrent aggressive or indolent B-cell lymphoma or CLL, or newly diagnosed patients unable to receive or complete standard therapy OR diagnosis of relapsed/refractory aggressive B-cell lymphoma with a treatment plan that will include high dose therapy and autologous stem cell transplantation No prior treatment for mantle cell lymphoma with the exception of corticosteroids for 7 days or less, or 1 course of involved-field radiation Patients with primary tumors including germ cell tumor, or lymphoma/leukemia Pathologically confirmed T-cell lymphomas at the enrolling institution, including stage >= Ib cutaneous T-cell lymphoma (CTCL), which has relapsed or progressed after at least one systemic therapy Receiving systemic therapy for another primary malignancy (other than T-cell lymphoma);\r\n* Patients with more than one type of lymphoma may be enrolled after discussion with the MSK principal investigator\r\n* Adjuvant or maintenance therapy to reduce the risk of recurrence of other malignancy (other than T-cell lymphoma) is permissible after discussion with the MSK principal investigator The following histologies will need to be confirmed at Memorial Sloan-Kettering Cancer Center (MSK) or locally for participating sites in order to be considered for HDT-ASCT and post-transplant maintenance romidepsin:\r\n* Peripheral T-cell lymphoma (PTCL)\r\n* Angioimmunoblastic T-cell lymphoma (AITL)\r\n* Anaplastic large-cell lymphoma (ALCL)\r\n* Enteropathy-associated T-cell lymphoma (EaTCL)\r\n* Hepatosplenic gamma delta T-cell lymphoma\r\n* Adult T-cell leukemia/lymphoma\r\n* Primary cutaneous gamma/delta T-cell lymphoma\r\n* Extranodal natural killer (NK)/T-cell lymphoma, nasal type\r\n* Primary cutaneous anaplastic large cell lymphoma\r\n* Subcutaneous panniculitis-like T-cell lymphoma\r\n* Mycosis fungoides/Sezary syndrome Recipients (patients with B-cell malignancy) must have received an human leukocyte antigen (HLA)-identical sibling allogeneic hematopoietic stem cell transplant, or a >= 9/10-matched unrelated donor (URD) alloHSCT for any CD19+ B-cell malignancy; haploidentical donors will not be used in this protocol; patients with any CD19+ B-cell malignancy that is persistent or relapsed after all of the following interventions are eligible:\r\n* Donor T cell engraftment after alloHSCT (> 50% donor chimerism of the T cell compartment and a peripheral blood T cell number from the National Institutes of Health (NIH), Clinical center (CC) clinical lab of at least 50 CD3+ cells/uL)\r\n* A trial of withdrawal of immunosuppressive therapy\r\n* At least one donor cell infusion (DCI) with a minimum T cell dose of 5 x 106 CD3+ cells/kg; Exception: prior DCI (donor lymphocyte infusion [DLI]) is not an eligibility requirement for patients with acute lymphopblastic leukemia (ALL), Burkitt lymphoma, ALL-like high-grade lymphomas, or diffuse large B-cell lymphoma\r\n** NOTE: at least 28 days must have elapsed since the latest trial of withdraw of immunosuppression or DCI until the patient can be deemed to have persistent disease 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 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 Large cell lymphoma, mantle cell lymphoma and Hodgkin disease that is progressive on salvage therapy; stable disease is acceptable to move forward provided it is non-bulky Any stage for mediastinal gray zone lymphoma (MGZL) and primary mediastinal B cell lymphoma (PMBL) Large cell lymphoma, mantle cell lymphoma and Hodgkin disease that is progressing on salvage therapy Any high grade B-cell lymphoma Histologically confirmed peripheral T-cell lymphoma (PTCL) as defined by the World Health Organization (WHO) criteria 2016, excluding cutaneous T-cell lymphoma (CTCL); transformed mycosis fungoides is allowed Patients with B-cell lymphoma who are candidates to autologous stem-cell transplantation, including: 1. Primary refractory or relapsed diffuse large B-cell lymphoma in response to salvage treatment. 2. Primary refractory or relapsed follicular lymphoma or other indolent B-cell histology in response to salvage treatment. 3. Chemosensitive mantle-cell lymphoma in first or later line of treatment. 4. Patients with B cell lymphoma (all CD19+ NHL) with progressive or refractory disease who would otherwise not be candidates for autologous stem cell transplantation Patients must have a histologically documented (either primary or metastatic site) diagnosis of advanced solid tumor cancer (stage IV or unresectable) or aggressive lymphoma (diffuse large B cell lymphoma, mantle cell lymphoma, T cell lymphoma, and natural killer [NK] cell lymphoma)\r\n* NOTE: The following histologies will be excluded: non-small cell lung cancer, squamous cell carcinoma of head and neck, melanoma, renal cell carcinoma, bladder cancer, Hodgkin’s lymphoma, Merkel cell carcinoma, and high-frequency microsatellite instability (MSI-H) colorectal cancer\r\n* NOTE: Patients with deleterious BRCA 1/2 mutated ovarian cancer will be excluded Have a histologically or cytologically confirmed relapsed/refractory mature T-cell lymphoma that has progressed after a minimum of 1 systemic therapy with any of the following T-cell histologies: peripheral T-cell non-Hodgkin lymphoma (NHL), not otherwise specified (PTCL, NOS); anaplastic large cell T-cell lymphoma (ALCL) anaplastic lymphoma kinase positive or negative; angioimmunoblastic T-cell lymphoma; subcutaneous panniculitis like T-cell lymphoma; primary cutaneous gamma-delta T cell lymphoma; enteropathy associated T-cell lymphoma; hepatosplenic T-cell lymphoma; extranodal NK/T-cell lymphoma, nasal type; adult T-cell leukemia/lymphoma; unclassifiable PTCL; and transformed cutaneous T-cell lymphoma (CTCL) to PTCL with systemic involvement (not local skin transformation) Biopsy proven NHL, including plasmablastic lymphoma and primary effusion lymphoma but not T-cell lymphoma; tissue histology will be reviewed at City of Hope (COH); patients who have been in remission for >= 1 year post Hodgkin's lymphoma chemotherapy are also considered eligible Recurrent B cell lymphoma or leukemia (ALL or CLL), or newly diagnosed patients unable to receive or complete standard therapy OR diagnosis of relapsed/refractory intermediate B cell lymphoma with a treatment plan that will include high dose therapy and autologous stem cell transplantation; if the patient is less than age 18, the lymphoma/leukemia is highly aggressive (i.e. lymphoblastic, Burkitt, ALL) Mature T-cell lymphoma\r\n* T-cell lymphomas including primary T-cell not otherwise specified, angioimmunoblastic, and anaplastic lymphoma kinase (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 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 Patients with Burkitt's lymphoma/leukemia (i.e. patients with mature B-cell ALL, leukemia with B-cell [surface Immunoglobulin (sIg) positive and kappa or lambda restricted positivity] ALL, with FAB L3 morphology and /or a MYC translocation) Phase 2 subjects with known lymphoma: >=1000 cells/mm3 (>750 cell/mm3 for subjects with lymphoma in bone marrow) T-cell lymphoma Patients with Burkitt's lymphoma/leukemia (i.e. patients with mature B-cell ALL, leukemia with B-cell [sIg positive and kappa or lambda restricted positivity] ALL, with FAB L3 morphology and /or a MYC translocation) Cohort 5: Participants must have a mature T cell, B cell, or natural killer (NK) cell neoplasm. Primary mediastinal B-cell lymphoma Patients must have histologically confirmed relapsed or refractory mantle cell lymphoma or low grade B-cell non-Hodgkin lymphoma (NHL); patients with evidence of transformation to a high grade histology will not be eligible Mantle cell lymphoma International Prognostic Index (IPI) (MIPI) score must be calculated and entered in Oncology Patient Enrollment Network (OPEN)\r\n* NOTE: for this calculation white blood cell (WBC) 7,500/mm^3 = 7,500/uL = 7.5 x 10^9/L should be entered as 7500 Pathologically confirmed T or NK cell lymphoma at the enrolling institution; for cutaneous T-cell non-Hodgkin lymphoma (CTCL), patients with stage IB disease or greater are eligible Previous systemic anti-cancer therapy for T-cell lymphoma must have been discontinued at least 2 weeks prior to treatment;\r\n* Glucocorticoids aimed at controlling lymphoma-related symptoms are allowed as long as they are tapered down to 20 mg or less by the time of ruxolitinib initiation\r\n* Topical steroids for CTCL are permitted Receiving systemic therapy for another primary malignancy (other than T-cell lymphoma)\r\n* Patients with more than one type of lymphoma may be enrolled after discussion with the Memorial Sloan-Kettering (MSK) principal investigator\r\n* Adjuvant or maintenance therapy to reduce the risk of recurrence of other malignancy (other than T-cell lymphoma) is permissible after discussion with the MSK principal investigator Any previous chemotherapy or radiation for mantle cell lymphoma; short course of steroids for symptom relief prior to presentation is permissible Histologically confirmed new diagnosis of stage II, III and IV peripheral T-cell non-Hodgkin’s lymphoma not otherwise specified (NOS), anaplastic large cell lymphoma (ALK negative) (ALK positive if IPI 3, 4, or 5), angioimmunoblastic T-cell lymphoma, enteropathy associated T-cell lymphoma, hepatosplenic gamma delta T-cell lymphoma Patients with a diagnosis of other peripheral T-cell lymphoma (PTCL) histologies other than those specified in the inclusion criteria Patients with non-T-cell-based lymphoma of any type or hairy cell leukemia are eligible on the condition that they do not receive active systemic treatment for their hematologic disease and are in complete remission as evidenced by PET/CT scans and bone marrow biopsies for at least 3 months. Pathologically confirmed B- or T-cell lymphomas at the enrolling institution, including stage >= Ib cutaneous T-cell lymphoma (CTCL), which has relapsed or progressed after at least one systemic therapy\r\n* Hodgkin lymphoma is allowed and will be classified as a B-cell lymphoma in the phase IIA portion Patients must have a confirmed diagnosis of mantle cell lymphoma with positivity in tissue biopsy All patients must have a pathologic diagnosis of one of the following malignancies:\r\n* Non-Hodgkin’s lymphoma, including B- and T-cell lymphoma\r\n* Multiple myeloma or another plasma cell dyscrasia (Waldenstrom, Amyloidosis) Histologically confirmed mantle cell lymphoma (MCL) Relapse or progression after at least one systemic therapy for mantle cell lymphoma Inclusion Criteria:\n\n • Aged 18 years or older, with lymphoid malignancies of B-cell origin as follows:\n\n *Indolent / aggressive B-cell (NHL) Non- Hodgkin's Lymphoma:\n\n EXCLUDING: Burkitt lymphoma and precursor B-lymphoblastic leukemia/lymphoma\n\n INCLUDING: any non-Hodgkin's B-cell malignancy such as CLL and rare non-Hodgkin's B-cell\n subtypes such as Hairy Cell Leukemia, Waldenstrom macroglobulinemia, Mantle cell lymphoma,\n transformed NHL histologies, etc.\n\n *Hodgkin's lymphoma\n\n - Life expectancy of 12 weeks or longer.\n\n - Subject must have received ? 1 prior treatment regimen.\n\n - The subject must not be a candidate for potentially curative therapy, including stem\n cell transplant.\n\n Exclusion Criteria:\n\n - Received an investigational study drug within 28 days or 5 half-lives (whichever is\n longer) prior to receiving the first dose of study drug.\n\n - Received any approved anticancer medications within 21 days or 5 half-lives (whichever\n is longer) prior to receiving their first dose of study drug (42 days for\n nitrosoureas) EXCEPT steroids at ? 10 mg prednisone daily (or equivalent).\n\n - Has any unresolved toxicity ? Grade 2 from previous anticancer therapy.\n\n - Has history of brain metastases or spinal cord compression, or lymphoma involving the\n central nervous system.\n\n - Has an Eastern Cooperative Oncology Group (ECOG) performance status of ? 3.\n\n - Received allogeneic hematopoietic stem cell transplant within the last 6 months, or\n has active graft versus host disease (GVHD) following allogeneic transplant, or is\n currently receiving immunosuppressive therapy following allogeneic transplant.\n\n - Received autologous hematopoietic stem cell transplant within the last 3 months.\n\n - Laboratory parameters not within the protocol-defined range.\n\n - Current or recent history (<30 days prior to screening and/or <45 days prior to\n dosing) of a clinically meaningful bacterial, fungal, parasitic or mycobacterial\n infection.\n\n - Current clinically active viral infection.\n\n - Known history of infection with the human immunodeficiency virus (HIV).\n\n - History of active hepatitis or positive serology for hepatitis. Patients with aggressive B-cell non-Hodgkin lymphoma subtypes including, relapsed or refractory diffused large B-cell lymphoma (DLBCL) and transformed follicular lymphoma meeting at least one of the following criteria:\r\n* Bone marrow involvement at the time of relapse or refractory disease and not appropriate for allogeneic transplantation\r\n* Positron emission tomography (PET) positive disease outside of one radiation port, unless single-port disease treated with prior radiotherapy within the port, following >= 2 cycles of salvage chemotherapy, per 1999 International Working Group (IWG) criteria Diagnosis of islet cell tumor, lymphoma, metastatic lesion, acinar cell (or other atypical pathologic malignancy) Pathology confirmed lymphoma or multiple myeloma\r\n* Hodgkin lymphoma is eligible for either phase and will be considered a B-cell lymphoma in the phase IIa study\r\n* Phase IIa portion, subjects must have B-cell lymphoma, T-cell lymphoma, or multiple myeloma Have a clinical diagnosis of cutaneous T cell lymphoma CTCL, including documentation of a skin biopsy within the prior 3 years with histological findings consistent with CTCL (atypical epidermotropic or folliculocentric T-cells) Indolent B-cell NHL lymphoma (study part B): Patient with radiosensitive histologies (lymphoma, multiple myeloma, small cell carcinomas, germ cell tumors) Male or female participants 18 years or older with diagnosis of mycosis fungoides (MF) or primary cutaneous anaplastic large cell lymphoma (pcALCL) No prior radiation therapy for mantle cell lymphoma Patients with histologically confirmed aggressive B-cell lymphoid malignancy, such as diffuse large B cell lymphoma (DLBCL), including primary mediastinal large B cell lymphoma, T cell rich B cell lymphoma, \double hit\ DLBCL, mantle cell lymphoma, any transformed low grade B cell lymphomas or grade 3 follicular lymphoma (grade 3a or 3b) who were refractory to rituximab-cyclophosphamide-hydroxydaunorubicin (doxorubicin hydrochloride)-Oncovin (vincristine sulfate)-prednisone (R-CHOP)-like or any anthracycline based chemotherapy or relapsed after at least one prior combination chemotherapeutic regimen and who are deemed candidates for a salvage type chemotherapy\r\n* Relapsed disease:\r\n** Progressive disease after a CR for at least 28 days; progression will be defined according to the Revised Response Criteria for Malignant Lymphoma (Cheson 2007)\r\n* Refractory disease:\r\n** Subjects must meet one of the following criteria:\r\n*** Persistent or progressive lymphoma with a CR of < 28 days duration or with a PR of any duration; subjects must have received at least 3 cycles of RCHOP-like or any anthracycline base chemotherapy or at least 2 full cycles of hyperfractionated cyclophosphamide-vincristine sulfate-Adriamycin (doxorubicin hydrochloride)-dexamethasone (HyperCVAD)-like chemotherapy\r\n*** Persistent lymphoma and stable disease after at least 2 cycles of RCHOP-like or any anthracycline base chemotherapy or at least 1 full cycle of HyperCVAD-like chemotherapy (part A and B)\r\n*** Progressive disease despite at least 1 cycle of RCHOP-like or any anthracycline base chemotherapy or at least 1 cycle (part A or A and B) of HyperCVAD-like chemotherapy Primary germ cell tumor, small cell carcinoma, or lymphoma Have confirmed mantle cell lymphoma diagnosis. Persistent, or relapsed non-Hodgkin's lymphoma (NHL) (any histology) that is chemo-resistant (< a partial response [PR]), subjects who have received >= 3 prior chemotherapy regimens, or subjects with lymphomas that have a high relapse rate following autologous or syngeneic stem cell transplantation (transformed NHL, peripheral T-cell lymphoma [PTCL], mantle cell lymphoma, anaplastic lymphoma kinase [ALK]-negative anaplastic large cell lymphoma [ALCL, alk neg]), intermediate International Prognostic Index (IPI) or high risk IPI or subjects with a positive positron emission tomography (PET) scan prior to transplant, and otherwise eligible for transplantation with adequate end-organ function Chemosensitive NHL, except subjects receiving >= 3 prior chemotherapy regimens, or subjects having transformed NHL, PTCL, mantle cell lymphoma (MCL) or ALCL, alk neg 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 T-cell neoplasm: adult T-cell leukemia/lymphoma, hepatosplenic T-cell lymphoma, and enteropathy associated T-cell lymphoma\r\n* First CR\r\n* Chemotherapy-refractory disease\r\n* Relapse after greater than or equal to 1 prior regimen For patient with NK cell neoplasms: 1) 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; 2) all NK cell neoplasms can be transplanted in: a) primary induction failure or b) second or greater complete remission For patients with T-cell neoplasms including adult T-cell leukemia/lymphoma, hepatosplenic T-cell lymphoma and enteropathy associated T-cell lymphoma\r\n* First CR\r\n* Chemotherapy-refractory disease\r\n* Relapse after greater than or equal to 1 prior regimen Patients with CD30 positive Hodgkin lymphoma (HL) or anaplastic large cell lymphoma (ALCL) that have undergone allogeneic or haploidentical stem cell transplant (SCT) in the past 60 days (matched related or matched unrelated donors only) Hodgkin's variant of Richter's lymphoma, accelerated CLL, composite lymphoma, interdigitating dendritic cell sarcoma, sarcoma, EBV-associated lymphoma or prolymphocytic transformation. Patients must have histologically proven T-cell lymphoma, including the following subtypes:\r\n* Peripheral T-cell lymphoma, not otherwise specified\r\n* Angioimmunoblastic T-cell lymphoma\r\n* Anaplastic large cell lymphoma, anaplastic lymphoma receptor tyrosine kinase (ALK) positive\r\n* Anaplastic large cell lymphoma, ALK negative\r\n* Mycosis fungoides\r\n* Sezary syndrome T-cell primary CNS lymphoma. Confirmed diagnosis of mantle cell lymphoma Confirmed diagnosis of PTCL expressing CD30 receptor; diagnosis will be based on identification of PTCL in biopsy specimens characterized 0 (negative) to 79% (positive) immunohistochemistry staining with CD30 in the malignant cell population; following PTCL subtypes will be eligible: \r\n* Peripheral T-cell lymphoma, not otherwise specified (NOS) \r\n* Angioimmunoblastic T-cell lymphoma \r\n* Subcutaneous panniculitis like T-cell lymphoma \r\n* Hepatosplenic gamma/delta T-cell lymphoma \r\n* Extranodal natural killer (NK) T-cell lymphoma, nasal type \r\n* Enteropathy-associated T-cell lymphoma \r\n* Adult T-cell leukemia/lymphoma \r\n* T-cell prolymphocytic leukemia \r\n* Primary cutaneous gamma-delta T-cell lymphoma \r\n* Aggressive NK cell leukemia \r\n* Aggressive subtype of T cell large granular lymphocyte (LGL) leukemia or transformed LGL leukemia\r\n* Epstein-Barr virus (EBV)-positive T-cell lymphoproliferative disorders of childhood \r\n* Transformed mycosis fungoides who have progressed following treatment with at least one systemic therapy\r\n* Sezary syndrome \r\nImmunophenotyping of lymphomas will be performed with panels of monoclonal antibodies targeting surface markers and assisting in differential diagnosis of PTCL according to National Comprehensive Cancer Network (NCCN) guidelines version (V)2 2012; CD2, CD5, CD7, CD4, CD8, CD10, CD25, CD30, CD56, beta-Framework 1 (F1), activin receptor-like kinase-1 (ALK-1), Epstein-Barr virus encoded ribonucleic acid (RNA) (EBER), TIA1 cytotoxic granule-associated RNA binding protein (Tia-1), granzyme B, cartesian genetic programming (CGP), perforin, CD21, B-cell chronic lymphocytic leukemia/lymphoma 6 (bcl-6), programmed cell death 1 (PD-1); proliferation index will also be evaluated using antibodies against mindbomb E3 ubiquitin protein ligase 1 (Mib-1)/ marker of proliferation Ki-67 (Ki-67); clonality studies with T-cell receptor (TCR) gene rearrangement of beta and gamma genes will also be included; pathology sample must be adequate for a complete immunohistochemical analysis Biopsy-confirmed relapsed, refractory, or progressive NHL or HL, including cutaneous T-cell lymphoma (CTCL) Patient has one of the following peripheral T-cell lymphoma (PTCL) subtypes confirmed by an independent central pathology reviewer, using the Revised European American Lymphoma World Health Organization disease classification: T/natural killer (NK)-cell leukemia/lymphoma Anaplastic large cell lymphoma (ALCL), primary systemic type, excluding anaplastic lymphoma kinase positive (ALK+) with International Prognostic Index (IPI) score less than 2 at initial diagnosis and complete response (CR) after CHOP-based therapy Enteropathy-type intestinal lymphoma Extranodal T/NK-cell lymphoma nasal or nasal type High grade B-cell lymphoma (HGBCL) Any T cell lymphoma In addition, cutaneous B and T cell lymphoma are permitted; cutaneous T cell lymphoma must be refractory to 1 prior systemic therapy (topical therapy, photophoresis, radiation are not considered systemic therapy); transformed B and T cell cutaneous lymphoma are also permitted Relapsed/refractory nodal, leukemic, and extranodal T cell lymphomas are eligible; subtypes eligible include anaplastic large cell lymphoma, angioimmunoblastic T cell lymphoma, peripheral T-cell lymphoma-not-otherwise specified (PTCL-NOS), nasal or disseminated extranodal T/natural killer (NK) lymphoma, enteropathy-associated T cell lymphoma, hepatosplenic gamma/delta T cell lymphoma, subcutaneous panniculitis-like T cell lymphoma, T-prolymphocytic leukemia, adult T-cell leukemia/lymphoma, large granular lymphocytic leukemia, aggressive NK leukemia Enteropathy-Associated T cell Lymphoma (EATL) Primary disease of hematologic origin, lymphoma, or small cell cancer Patients with non-Hodgkin’s lymphoma and one or more of the following: \r\n* Diffuse large B-cell lymphoma with one or more of the following: \r\n** Primary refractory disease\r\n** Relapse within 12 months of completion of first-line therapy\r\n** Secondary International Prognostic Index (IPI) > 1\r\n** Less than partial remission (PR) to first-line salvage chemotherapy\r\n** Kinetic failure after salvage chemotherapy\r\n** Prior treatment with 3 or more lines of therapy\r\n** Patients with double-hit or triple-hit non-Hodgkin lymphoma (NHL), in any state of the disease\r\n* Peripheral T-cell lymphoma not otherwise specified (PTCL-NOS) in any stage of the disease\r\n* Angioimmunoblastic T-cell lymphoma (AITL) in any stage of the disease\r\n* Refractory or recurrent Burkitt¹s lymphoma\r\n* Any other lymphoma that is refractory or relapsed and that does not qualify for treatment protocols of higher priority Participants must have histologically confirmed peripheral T-cell lymphoma, with the diagnostic specimen reviewed at one of the Dana-Farber Harvard Cancer Center (DFHCC) hematopathology laboratories; eligible histologies include:\r\n* PTCL-not otherwise specified (NOS)\r\n* Systemic T cell/null anaplastic large cell lymphoma (ALCL), regardless of anaplastic lymphoma kinase (Alk)-status\r\n* Angioimmunoblastic T-cell lymphoma (AITL)\r\n* Hepatosplenic (alpha-beta or gamma-delta) lymphoma (HSL)\r\n* Enteropathy-associated T-cell lymphoma (EATL)\r\n* Adult T-cell leukemia/lymphoma (ATLL), lymphomatous subtype\r\n* Subcutaneous panniculitis-like T-cell lymphoma\r\n* T-cell prolymphocytic leukemia (T-PLL)\r\n* Natural killer (NK) cell lymphoma/leukemia Patients with extranodal NK T-cell lymphoma B-cell lymphoma with comprehensive immunohistochemistry (IHC) panel establishing lineage (cluster of differentiation [CD]20, CD3) and cell of origin (CD10, B-cell chronic lymphocytic leukemia [CLL]/lymphoma 6 [BCL6] and melanoma associated antigen [mutated] 1 [MUM1]) in addition to proliferative/prognostic markers (proliferation-related Ki-67 antigen [Ki-67], C-myc and B-cell CLL/lymphoma 2 [BCL2]); DHL will be identified using cytogenetics and/or immunohistochemistry as detailed in DHL defined below One of the following poor-risk lymphomas or plasma cell neoplasms, in PR or better prior to transplantation:\r\n* Transformed lymphoma\r\n* T-cell prolymphocytic leukemia (PLL)\r\n* Peripheral T-cell lymphoma\r\n* Natural killer (NK) or NK/T-cell lymphoma\r\n* Blastic/blastoid mantle cell lymphoma\r\n* Plasma cell leukemia Treatment-naive CD30-positive mature T-cell and NK-cell neoplasms, including systemic anaplastic large cell lymphoma Current diagnosis of primary cutaneous anaplastic large cell lymphoma, mycosis fungoides, Sezary syndrome or other primary cutaneous lymphomas; extranodal NK/T-cell lymphoma, nasal type Histologically confirmed cancer with 1-4 brain metastases (except lymphoma or small cell histologies) mantle cell lymphoma Meets one of the following need-for-treatment criteria (with the exception of mantle cell lymphoma for which treatment is indicated): Patients must be newly diagnosed with mantle cell lymphoma, have an accessible disease site for excisional biopsy or have sufficient peripheral blood tumor to leukapheresis at least 1.5 x 10^9 lymphoma cells in a single session Documentation of diagnosis as evidenced by one or more clinical features consistent with mycosis fungoides cutaneous T-cell lymphoma Burkitt, mantle cell, follicular, or mucosa-associated lymphoid tissue lymphoma Previously untreated mantle cell lymphoma patients (at least clinical stage 2) Platelet count >= 100,000, unless felt to be secondary to underlying mantle cell lymphoma Patients with mantle cell lymphoma (MCL) with stage 1 or 2 disease Large cell lymphoma, mantle cell lymphoma and Hodgkin disease that is progressing on salvage therapy Patients must have histologically or cytologically confirmed (at original diagnosis or subsequent recurrence or progression) lymphoma, chronic lymphocytic lymphoma (CLL) or solid tumor; patients with lymphoma or CLL must have radiologically or clinically evaluable disease, and be refractory to standard therapy as defined by relapse within 6 months of last treatment (see note below); patients with solid tumors must have radiologically or clinically evaluable disease that is metastatic, unresectable, progressive, or recurrent, and for which standard curative measures do not exist or are no longer effective\r\n* Patients with a liver mass, raised alpha-fetoprotein level (>= 500 ng/mL) and positive serology for hepatitis, consistent with a diagnosis of hepatocellular carcinoma will be eligible without the need for pathologic confirmation of the diagnosis\r\n* Patients with prostate cancer, renal cell cancer, neuroendocrine tumors, lung cancer, colorectal cancers, soft tissue sarcomas, glioma and thyroid cancer are excluded in the normal and mild cohorts due to a lack of efficacy in these tumor types in phase 2 studies; patients with breast, pancreatic, bladder, head and neck cancers, as well as melanoma and other malignancies are eligible\r\n* Note: patients with prostate cancer, renal cell cancer, lung cancer, colorectal cancers, soft tissue sarcomas, glioma and thyroid cancer are allowed to enroll in the moderate and severe cohorts provided the patients:\r\n** Sign a separate consent form which outlines the lack of efficacy observed in prior studies\r\n** Are consented to the study by a protocol-specified designee who is not their longitudinal oncologist; patients with neuroendocrine tumors are still excluded from the moderate and severe cohorts\r\n* Note: as romidepsin is approved for patients with relapsed or refractory peripheral T-cell lymphoma (PTCL) or cutaneous T cell lymphoma (CTCL), these patients would be eligible WITHOUT the requirement of having ‘relapsed within 6 months of last treatment’ High grade B-cell lymphoma with MYC and BCL2 and/or BCL6 rearrangements with DLBCL histology (double/triple-hit lymphoma) For the Dose Escalation phase, participants must have histologically confirmed diagnosis of advanced NHL of any histology (with the exception of participants with mantle cell lymphoma [MCL] or chronic lymphoma leukemia [CLL]). B-cell ALL CNS3 leukemia Patients with known active CNS leukemia. Known central nervous system (CNS) leukemia. Clinical evidence of active central nervous system leukemia; COHORT 1: Has known active central nervous system (CNS) leukemia; subjects with previously treated CNS leukemia may participate provided that they have documented clearance of CNS leukemia and are not actively treated with intrathecal chemotherapy COHORT 2: Has known active central nervous system (CNS) leukemia; subjects with previously treated CNS leukemia may participate provided that they have documented clearance of CNS leukemia and are not actively treated with intrathecal chemotherapy Have active central nervous system (CNS) leukemia Participants with known central nervous system (CNS) leukemia involvement should be excluded from this clinical trial; patients with a history of CNS leukemia that has been treated and is no longer active as judged by the treating investigator are eligible Active central nervous system (CNS) leukemia Active, uncontrolled central nervous system (CNS) disease including CNS leukemia Presence of active central nervous system (CNS) leukemia. Subjects adequately treated for CNS leukemia documented by 2 consecutive cerebrospinal fluid samples negative for leukemia cells are eligible. Subjects with no history of CNS leukemia will not be required to undergo cerebrospinal fluid sampling for eligibility. Presence of active untreated central nervous system (CNS) leukemia Presence of known central nervous system (CNS) leukemia. Patients with symptomatic CNS leukemia or patients with poorly controlled CNS leukemia Patients with active central nervous system (CNS) leukemia eligible at the discretion of treating physician Patients with symptomatic CNS leukemia or patients with poorly controlled CNS leukemia. Clinical symptoms suggestive of active central nervous system (CNS) leukemia or known CNS leukemia. Evaluation of cerebrospinal fluid (CSF) during screening is required only if there is a clinical suspicion of CNS involvement by leukemia during screening. Patients with active, uncontrolled central nervous system (CNS) leukemia will not be eligible Active central nervous system (CNS) leukemia at time of treatment Known central nervous system (CNS) leukemia Patients with known active uncontrolled central nervous system (CNS) leukemia. Patients with current evidence of active central nervous system (CNS) leukemia Patients with symptomatic CNS leukemia or patients with poorly controlled CNS leukemia Patients with known active uncontrolled central nervous system (CNS) leukemia Patients with active central nervous system leukemia or requiring maintenance intrathecal chemotherapy If prior central nervous system (CNS) leukemia, it must be treated and in CNS CR Symptomatic and refractory central nervous system (CNS) leukemia Active leukemia in the central nervous system (CNS) Active uncontrolled central nervous system (CNS) leukemia; NOTE: positive (cyto)pathology is allowed and patient can receive intrathecal chemotherapy Patients must not have active central nervous system leukemia; patients with history of central nervous system (CNS) leukemia with no evidence of active CNS disease may be enrolled; maintenance intrathecal chemotherapy for adequately treated CNS involvement with leukemia is allowed with approval from the study supporter Individuals with CNS 3 leukemia Active central nervous system leukemia Active and/or untreated central nervous system (CNS) leukemia Patients with symptomatic CNS leukemia or patients with poorly controlled CNS leukemia Clinically active central nervous system leukemia. Clinical evidence of active central nervous system (CNS) leukemia requiring active therapy; prior CNS leukemia well-controlled by ongoing therapy is allowed Active central nervous system (CNS) leukemia Patients who have active central nervous system (CNS) disease; patients with previously treated leptomeningeal disease without evidence of remaining leukemia cells by spinal fluid will be eligible No evidence of extramedullary leukemia, such as central nervous system (CNS) or soft tissue involvement Presence of leukemia in the central nervous system (CNS) Known clinically active central nervous system (CNS) or extramedullary AML, except leukemia cutis. Have active central nervous system (CNS) leukemia Presence of leukemia in the central nervous system (CNS) Active central nervous system (CNS) leukemia at time of HCT Evidence of active extramedullary disease (including central nervous system [CNS] leukemia) Active central nervous system (CNS) leukemia at time of HSCT Clinical symptoms suggesting active central nervous system (CNS) leukemia or known CNS leukemia Clinically active central nervous system (CNS) leukemia; CNS leukemia Has central nervous system (CNS) involvement of leukemia or a history of CNS leukemia Known central nervous system leukemia Known clinically active central nervous system (CNS) leukemia Known clinically active central nervous system(CNS) leukemia Who have active central nervous system (CNS) disease; patients with previously treated leptomeningeal disease without evidence of remaining leukemia cells by spinal fluid will be eligible Patients with known or suspected central nervous system (CNS) leukemia are not eligible Patients with known central nervous system infiltration with leukemia Have clinical symptoms suggestive of active central nervous system (CNS) leukemia or known CNS leukemia. Subjects must not have evidence of active leukemia in the central nervous system (CNS) Active central nervous system (CNS) leukemia Patients with suspected or proven central nervous system (CNS) leukemia; (diagnostic lumbar puncture not required before enrollment) Active or suspicion of central nervous system (CNS) leukemia Subject has clinically active central nervous system leukemia. Subjects with clinical symptoms suggesting active central nervous system (CNS) leukemia or known CNS leukemia. Evaluation of cerebrospinal fluid is only required if there is a clinical suspicion of CNS involvement by leukemia during screening. Known CNS lymphoma or leukemia. Known CNS lymphoma or leukemia. Active CNS leukemia Proven Central Nervous System (CNS) leukemia Patients with known active uncontrolled central nervous system (CNS) leukemia. Patients with symptomatic CNS leukemia or patients with poorly controlled CNS leukemia Evidence of active central nervous system (CNS) leukemia Patients with active/uncontrolled central nervous system (CNS) leukemia Subject has clinically active central nervous system leukemia. Active central nervous system (CNS) leukemia or known CNS leukemia. Central nervous system (CNS) leukemia Active uncontrolled central nervous system (CNS) leukemia; NOTE: positive (cyto)pathology is allowed and patient can receive intrathecal chemotherapy Patient has central nervous system leukemia Clinical evidence of active central nervous system (CNS) leukemia Subject has clinically active central nervous system leukemia. Clinical evidence of active central nervous system leukemia at the time of screening Subjects with clinical symptoms suggesting active central nervous system (CNS) leukemia or known CNS leukemia. Active central nervous system (CNS) leukemia within two weeks of registration; patients with a history of CNS leukemia must have adequate treatment as defined by at least two negative spinal fluid assessments separated by at least one week; patients who have received cranial radiation therapy (XRT) must still be eligible to receive total body irradiation to 4 Gy Clinical evidence of active CNS leukemia Patient must not have known central nervous system (CNS) leukemia Active central nervous system (CNS) leukemia Known clinically active central nervous system (CNS) leukemia Presence of leukemia in the central nervous system (CNS) Patients with active and/or untreated central nervous system (CNS) leukemia will not be eligible Active or prior central nervous system (CNS) leukemia, unless in complete remission for at least 3 months Active central nervous system (CNS) leukemia at time of treatment Active central nervous system (CNS) leukemia Active, symptomatic central nervous system (CNS) leukemia; Patients with known active central nervous system (CNS) leukemia Previous central nervous system leukemia Patients with symptomatic central nervous system (CNS) leukemia or patients with poorly controlled central nervous system leukemia Active central nervous system (CNS) leukemia Known active central nervous system (CNS) leukemia. Patients with known active central nervous system (CNS) leukemia will be excluded from this clinical study Known active leukemia of the central nervous system Presence of central nervous system (CNS) leukemia. Current CNS Leukemia Known clinically active CNS leukemia If prior central nervous system (CNS) leukemia, it must be treated and in CNS complete remission (CR) Subject has clinically active central nervous system leukemia Current evidence of central nervous system (CNS) leukemia The patient has known active or suspected central nervous system (CNS) leukemia. If suspected, CNS leukemia should be ruled out with relevant imaging and/or examination of cerebrospinal fluid. For participants with leukemia, has overt central nervous system (CNS) disease (CNS 3 status). If prior central nervous system (CNS) leukemia, it must be treated and have no evidence of CNS disease CNS leukemia. Active central nervous system (CNS) leukemia or known chloromatous disease Active central nervous system (CNS) leukemia Overt central nervous system manifestations of leukemia at diagnosis Clinical evidence of central nervous system (CNS) or pulmonary leukostasis, or CNS leukemia Has presence of central nervous system (CNS) involvement of leukemia or a history of CNS leukemia Subject has clinically active central nervous system leukemia. Known active or suspected central nervous system (CNS) leukemia. Patients with active central nervous system leukemia are excluded from this clinical trial; patients with a history of central nervous system (CNS) leukemia but no active disease at the time of enrollment are eligible; the absence of CNS disease must be confirmed by flow cytometric and cytologic examination of the cerebrospinal fluid (CSF) within 7 days of study enrollment CNS leukemia Subjects with clinical symptoms suggesting active central nervous system (CNS) leukemia or known CNS leukemia. Evaluation of cerebrospinal fluid is only required if there is clinical suspicion of CNS involvement by leukemia during screening. Known active central nervous system (CNS) leukemia. Children who have histologically proven diagnoses of the following types of CNS tumor are eligible for entry onto this protocol; the exclusive focus is on medulloblastoma and other CNS primitive neuro-ectodermal tumors (PNET) of the brain or spinal cord All children less than 120 months (10years) of age, irrespective of clinical stage, with a diagnosis of any of the following CNS PNET are eligible: pineoblastoma, all primary CNS-PNET, including CNS/cerebral neuroblastoma, CNS/cerebral ganglioneuroblastoma, medulloepithelioma, ependymoblastoma, embryonal tumor with abundant neuropil and true rosettes (ETANTR; more recently designated as \embryonal tumor with multilayered rosettes\ or \ETMR\), melanotic medulloblastoma and/or medullomyoblastoma, CNS supratentorial PNET, spinal cord PNET, brainstem PNET are all eligible, regardless of patterns of (divergent) differentiation All diagnoses other than medulloblastoma and CNS PNET - these include: CNS atypical teratoid/rhabdoid tumor (AT/RT); all ependymomas including anaplastic ependymomas of the brain or spinal cord.; All choroid plexus carcinomas; all high-grade glial and glio-neuronal tumors; all primary CNS germ cell tumors; all primary CNS sarcomas; all primary or metastatic CNS lymphomas and solid leukemic lesions (i.e., chloromas, granulocytic sarcomas) Patients with CNS tumors or known CNS metastases will be excluded from this trial; patients with a history of CNS metastases that have been previously treated may enroll if sequential imaging shows not evidence for active disease; patients with extra axial disease (e.g. skull [bone] metastasis that do not invade the dura) may enroll if there is no evidence for CNS edema associated with the lesion Untreated CNS PTLD or CNS PTLD for which the subject is actively receiving treatment at enrollment Participants with primary CNS malignancies or tumors with CNS metastases as the only site of disease, will be excluded Acute symptomatic CNS hemorrhage Clinical Evidence of CNS disease CNS lymphoma. CNS status \r\n* Subjects with ALL\r\n** Subjects with the following CNS status are eligible only in the absence of neurologic symptoms suggestive of CNS leukemia, such as cranial nerve palsy:\r\n*** CNS 1, defined as absence of blasts in cerebral spinal fluid (CSF) on cytospin preparation, regardless of the number of white blood cells (WBCs)\r\n*** CNS 2, defined as presence of < 5/uL WBCs in CSF and cytospin positive for blasts, or > 5/uL WBCs but negative by Steinherz/Bleyer algorithm:\r\n**** CNS 2a: < 10/uL red blood cells (RBCs); < 5/uL WBCs and cytospin positive for blasts\r\n**** CNS 2b: >= 10/uL RBCs; < 5/uL WBCs and cytospin positive for blasts\r\n**** CNS 2c: >= 10/uL RBCs; >= 5/uL WBCs and cytospin positive for blasts but negative by Steinherz/Bleyer algorithm\r\n* Subjects with lymphoma\r\n** Subjects must have no signs or symptoms of CNS disease or detectable evidence of CNS disease on magnetic resonance imaging (MRI) at the time of screening; subjects who have previously been treated for CNS disease and who have the following CNS status will be eligible:\r\n*** CNS 1, defined as absence of blasts in cerebral spinal fluid (CSF) on cytospin preparation, regardless of the number of WBCs\r\n*** CNS 2, defined as presence of < 5/uL WBCs in CSF and cytospin positive for blasts, or > 5/uL WBCs but negative by Steinherz/Bleyer algorithm:\r\n**** CNS 2a: < 10/uL RBCs; < 5/uL WBCs and cytospin positive for blasts;\r\n**** CNS 2b: >= 10/uL RBCs; < 5/uL WBCs and cytospin positive for blasts;\r\n**** CNS 2c: >= 10/uL RBCs; >= 5/uL WBCs and cytospin positive for blasts but negative by Steinherz/Bleyer algorithm Subjects with radiologically-detected CNS lymphoma or CNS 3 disease (presence of >= 5/uL WBCs in CSF and cytospin positive for blasts [in the absence of a traumatic lumbar puncture] and/or clinical signs of CNS leukemia) Participants with primary CNS malignancies, or tumors with CNS metastases as the only site of disease, will be excluded Subjects with radiologically-detected active CNS lymphoma, leptomeningeal CNS disease or isolated CNS disease which are eligible for definitive CNS directed radiation therapy will be excluded Symptomatic or untreated Central nervous system (CNS) disease, Subjects with a history of CNS disease (leukemia, lymphoma or myeloma) are permitted to enrol if they have previously received appropriate therapy and CNS remission has been documented. Subject with primary CNS lymphoma (defined as isolated CNS lymphoma without systemic involvement) are excluded from study. TREATMENT WITH SJCAR19: CNS-1/CNS-2 disease with neurologic changes Active central nervous system (CNS) disease\r\n* Definition: any patient receiving active CNS therapy (defined as more than 1 intrathecal treatment per week or current radiation therapy to brain); if patient has a history of CNS disease: must have cerebrospinal fluid (CSF) sampling within 28 days of enrollment that is negative for leukemia; intrathecal chemotherapy for patients without active CNS disease is allowed (e.g., ongoing primary or secondary prophylaxis for patients who cleared the CSF prior to study enrollment); CSF sample is not required for enrollment for patients with no history of CNS disease Adequate central nervous system (CNS) function defined as:\r\n* Patients with seizure disorder may be enrolled if on allowed anti-convulsants and well controlled; benzodiazepines and gabapentin are acceptable\r\n* CNS toxicity < grade 2 Central nervous system (CNS) status\r\n* Subjects with leukemia with the following CNS status are eligible only in the absence of neurologic symptoms suggestive of CNS leukemia, such as cranial nerve palsy:\r\n** CNS 1, defined as absence of blasts in cerebral spinal fluid (CSF) on cytospin preparation, regardless of the number of white blood cells (WBCs)\r\n** CNS 2, defined as presence of < 5/uL WBCs in CSF and cytospin positive for blasts, or > 5/uL WBCs but negative by Steinherz/Bleyer algorithm:\r\n*** CNS 2a: < 10/uL red blood cells (RBCs); < 5/uL WBCs and cytospin positive for blasts\r\n*** CNS 2b: ? 10/uL RBCs; < 5/uL WBCs and cytospin positive for blasts\r\n*** CNS 2c: ? 10/uL RBCs; ? 5/uL WBCs and cytospin positive for blasts but negative by Steinherz/Bleyer algorithm\r\n* Subjects with lymphoma\r\n** Subjects must have no signs or symptoms of CNS disease or detectable evidence of CNS disease on magnetic resonance imaging (MRI) at the time of screening; subjects who have been previously treated for CNS disease but have no evidence of disease at screening are eligible Subjects with radiologically-detected CNS lymphoma or CNS 3 disease (presence of ? 5/uL WBCs in CSF and cytospin positive for blasts [in the absence of a traumatic lumbar puncture] and/or clinical signs of CNS leukemia and/or radiographic signs of leptomeningeal disease) Oral hydroxyurea and/or one dose of cytarabine (up to 2 g/m^2) for patients with rapidly proliferative disease is allowed before the start of study therapy and while the patient is on active study treatment through cycle 1, as needed, for clinical benefit and after discussion with the principal investigator (PI); concurrent therapy for central nervous system (CNS) prophylaxis or continuation of therapy for controlled CNS disease is permitted Concurrent therapy for central nervous system (CNS) prophylaxis or continuation of therapy for controlled CNS disease is permitted. Patients with a known history of CNS disease or leukemic brain metastasis must have been treated locally, have at least 3 consecutive lumbar punctures (LPs) with no evidence of CNS leukemia, and must be clinically stable for at least 4 weeks prior to enrollment and have no ongoing neurological symptoms that in the opinion of the treating physician are related to the CNS disease (sequelae that are a consequence of the treatment of the CNS disease are acceptable). Presence of CNS-3 disease or CNS-2 disease with neurological changes Concurrent therapy for extramedullary leukemia or central nervous system (CNS) lymphoma: Concurrent therapy or prophylaxis for testicular leukemia, CNS leukemia, and CNS lymphoma including standard intrathecal chemotherapy and/or radiation therapy will be allowed as clinically indicated. Such treatment may continue until the planned course is completed. Subjects must be in CNS remission at the time of protocol enrollment if there is a history of CNS involvement. Maintenance therapy after transplant is allowed Dose Escalation Cohorts: Active CNS disease, including history of CNS metastases. MTD/MFD Expansion Cohorts: CNS disease, including history of CNS metastases, that was not stable during the last 6 months. History of primary CNS malignancy, or leptomeningeal disease or CNS metastases CNS status \r\n* Subjects with ALL\r\n** Subjects with the following CNS status are eligible only in the absence of neurologic symptoms suggestive of CNS leukemia, such as cranial nerve palsy:\r\n*** CNS 1, defined as absence of blasts in CSF on cytospin preparation, regardless of the number of white blood cells (WBCs);\r\n*** CNS 2, defined as presence of < 5/uL WBCs in CSF and cytospin positive for blasts, or > 5/uL WBCs but negative by Steinherz/Bleyer algorithm:\r\n**** CNS 2a: < 10/uL red blood cells (RBCs); < 5/uL WBCs and cytospin positive for blasts;\r\n**** CNS 2b: >= 10/uL RBCs; < 5/uL WBCs and cytospin positive for blasts;\r\n**** CNS 2c: >= 10/uL RBCs; >= 5/uL WBCs and cytospin positive for blasts but negative by Steinherz/Bleyer algorithm\r\n* Subjects with DLBCL\r\n** Subjects must have no signs or symptoms of CNS disease or no detectable evidence of CNS disease on magnetic resonance imaging (MRI) at the time of screening; subjects who have been previously treated for CNS disease but have no evidence of disease at screening are eligible Known or suspected central nervous system (CNS) metastases, unless at least one month has passed since last local CNS therapy and there is no evidence for recurrent or progressive CNS disease on follow up imaging; participants may remain on steroids for CNS disease if they are taking a stable dose Patients with untreated, controlled asymptomatic central nervous system (CNS) lesions are allowed in this trial as long as the CNS is not a site of progressive disease on alectinib monotherapy; if the CNS is a site of progressive disease on alectinib monotherapy, treatment of CNS lesions is required for enrollment Participants who experienced progression of CNS lesions on alectinib who have not received local CNS therapies (radiation, surgery) to address the lesions; CNS imaging obtained at least 21 days after completion of radiation is required for confirmation of response Patients with history of central nervous system (CNS) metastases are eligible if CNS disease has been stable for at least 6 weeks prior to study registration in the opinion of the investigator and does not require corticosteroids (of any dose) for symptomatic management\r\n* NOTE: Only patients with a known history or indication of CNS disease are required to have CNS imaging prior to study entry Patients with a history of central nervous system (CNS) involvement by lymphoma or with relapsed primary CNS lymphoma will be eligible for cyclophosphamide (Cy)/TBI arm; patients with active CNS disease are eligible if they have completed a standard treatment for CNS lymphoma and have no evidence of progressive CNS disease at the time of enrollment Patients with evidence of active disease in the central nervous system (CNS) defined as either the presence of active lesions on MRI obtained within 4 weeks of registration or progressive neurological decline\r\n* Patients with primary CNS lymphoma who develop systemic recurrence following standard therapy may be included as long as no active CNS disease is present at the time or enrollment; similarly, patients with secondary involvement of the CNS from a systemic lymphoma may be included as long as the CNS disease has been optimally treated and they demonstrate no evidence of active CNS disease CELL PROCUREMENT: Lumbar puncture must be performed prior to procurement and subjects with evidence of CNS3 disease will be excluded from study entry; subjects with concurrent CNS3 disease and bone marrow relapse who have responded to CNS-directed therapy prior to enrollment/lymphodepletion will be allowed to participate; subjects with CNS2 disease and concurrent bone marrow relapse will be eligible; intrathecal chemotherapy will be allowed to continue between lymphodepleting chemotherapy and cell infusion In the absence of rapidly progressing disease, the interval from prior treatment to time of initiation of 5-azacytidine and avelumab will be at least 14 days OR at least 5 half-lives for cytotoxic/noncytotoxic agents, whichever is longer; the toxicity from prior therapy should have resolved to grade =< 1, however alopecia and sensory neuropathy grade =< 2 is acceptable; the half-life for the therapy in question will be based on published pharmacokinetic literature (abstracts, manuscripts, investigator brochures, or drug-administration manuals) and will be documented in the protocol eligibility document; use of hydroxyurea for patients with rapidly proliferative disease is allowed before the start of study therapy and will not require a washout; concurrent therapy for central nervous system (CNS) prophylaxis or continuation of therapy for controlled CNS disease is permitted; patients with CNS disease or leukemic brain metastasis must have been treated locally and be clinically stable for at least 2 weeks prior to enrollment and have no ongoing neurological symptoms that are related to the CNS disease (sequelae that are a consequence of the treatment of the CNS disease are acceptable) Subjects with history of central nervous system (CNS) disease are allowed if at the time of day 1 of the study there is no evidence of active CNS disease as documented by negative imaging or spinal fluid analysis carried out at least 2 weeks prior to the first study drug administration in a subject with no clinical signs of CNS disease Patients with history of central nervous system (CNS) lymphoma can be enrolled if the CNS disease has been controlled with therapy for a minimum of 4 weeks; brain magnetic resonance imaging (MRI) is not required for eligibility CNS disease that is progressive on therapy, or with CNS parenchymal lesions that might increase the risk of CNS toxicity Tumor lesions in the CNS are permitted but lesions must have been stable for at least 3 months prior to Cycle 1 Day 1 (C1D1). Stable CNS lesions are defined as not requiring steroid prophylaxis or other medications to prevent seizures or other complications associated with CNS lesions and no evidence of worsening of CNS disease. In the absence of rapidly progressing disease, the interval from prior treatment to time of initiation of selinexor and sorafenib administration will be at least 2 weeks for cytotoxic agents or at least 5 half-lives for cytotoxic/noncytotoxic agents; the use of chemotherapeutic or anti-leukemic agents is not permitted during the study with the following exceptions: (1) intrathecal (IT) therapy for patients with controlled central nervous system (CNS) leukemia at the discretion of the PI and with the agreement of the sponsor; controlled CNS leukemia is defined by the absence of active clinical signs of CNS disease and no evidence of CNS leukemia on the most recent 2 simultaneous cerebrospinal fluid (CSF) evaluations; (2) use of one dose of cytarabine (up to 2 g/m^2) or hydroxyurea for patients with rapidly proliferative disease is allowed before the start of study therapy and for the first four weeks on therapy; these medications will be recorded in the case-report form Relapsed/refractory leukemia in 2nd or greater relapse or who have failed at least one re-induction attempt after relapse or for refractory disease. Patients must meet the WHO classification with ? 5% blasts in the bone marrow or must have definitive extramedullary disease (e.g. chloromas, skin lesions). Patients may have asymptomatic CNS 1 or CNS 2 disease, but not CNS 3 or symptomatic CNS disease. OR Relapsed/refractory non-CNS solid tumor that has not responded or has relapsed and for which no standard treatment is available. Patients may not have primary CNS tumors or CNS metastases. Lymphoma patients are permitted. Patients do not need to have measurable disease. Patients with recurrent or progressive AT/RT or MRT (either CNS and/or extra-CNS) with radiographically measurable disease as defined by at least one lesion that can be measured in two dimensions or with tumor cells present in the CSF taken within 2 weeks prior to enrollment Patients with central nervous system (CNS) 1 or CNS 2 disease are eligible; patients with isolated CNS relapse or CNS 3 disease are not eligible Patients with non central nervous system (CNS) primary tumors who have known brain metastases or symptomatic CNS disease (e.g., cranial nerve abnormalities) without cytologic abnormality in the cerebrospinal fluid (CSF) should be excluded from this clinical trial; patients with metastatic CNS tumors will not be excluded from enrollment on this study in the phase I component only Patients with known central nervous system (CNS) disease are allowed if there is no evidence of active CNS disease as documented by negative imaging or spinal fluid analysis carried out at least 2 weeks prior to study drug administration; information obtained from standard of care historical data will be used for this purpose Concurrent therapy for extramedullary leukemia or central nervous system (CNS) lymphoma: concurrent therapy or prophylaxis for testicular leukemia, CNS leukemia, and CNS lymphoma including standard intrathecal chemotherapy and/or radiation therapy will be allowed as clinically indicated; such treatment may continue until the planned course is completed; subjects must be in CNS remission at the time of protocol enrollment if there is a history of CNS involvement Research participants with CNS involvement by leukemia, if deemed to be controlled and treatable by study team, at the time of enrollment are eligible; however, the CNS disease has to have been adequately treated with complete resolution of CNS leukemia confirmed by cerebral spinal fluid (CSF) analysis and imaging studies (if applicable) to be eligible to proceed with lymphodepletion Patients with active CNS disease Active CNS disease as identified by positive CSF cytospin at time of enrollment Patients with central nervous system (CNS) disease are eligible for treatment only after their CNS disease has been directly addressed with radiation therapy If prior CNS leukemia, it must be treated and in CNS complete remission (CR) Patients with active known CNS lymphoma. Patients with history of CNS leukemia now in remission are eligible for the trial. At the time of enrollment, specified baseline CNS conditions must be =< grade II toxicity per Common Terminology Criteria for Adverse Events (CTCAE) 3.0 criteria; this includes the following conditions: arachnoiditis/meningismus/radiculitis, ataxia, CNS cerebrovascular ischemia, CNS necrosis/cystid progression, cognitive disturbance, confusion, dizziness, encephalopathy, hydrocephalus, leak - cerebrospinal fluid, leukoencephalopathy (radiologic findings), mental status, psychosis, seizure, somnolence/depressed level of consciousness All patients with evidence of CNS leukemia must be treated and be in CNS CR to be eligible for study Patients must be free of active or ongoing ischemic or degenerative CNS disease and no active or resistant CNS leukemia CNS or testicular leukemia at diagnosis allowed Patients with a history of central nervous system (CNS) tumor involvement are eligible if they have completed treatment for CNS disease (radiotherapy or surgery or chemotherapy), have recovered from or stabilization of the side effects associated with the therapy and have no evidence of progressive CNS disease at the time of enrollment Serious underlying medical condition or infection other than HIV that would contraindicate SC-EPOCH-R; examples include, but are not limited to:\r\n* Severe AIDS-related wasting\r\n* Severe intractable diarrhea\r\n* Active inadequately treated opportunistic infection of the central nervous system (CNS)\r\n* Primary CNS lymphoma Primary CNS lymphoma Patients with active CNS disease History or clinical evidence of cnetral nervous system (CNS) HL Patients with metastatic disease limited to the CNS Patients with a history of ventral nervous system (CNS) myeloma or other CNS malignancy. Patients must have the status of CNS1 or CNS2 only, and no clinical signs or neurologic symptoms suggestive of CNS leukemia, such as cranial palsy Known leptomeningeal disease or CNS midline shifts Central nervous system (CNS) function defined as:\r\n* Patients with seizure disorder may be enrolled if on allowed anti-convulsants and well controlled; benzodiazepines and gabapentin are acceptable\r\n* CNS toxicity =< grade 2 Subject has symptomatic/untreated CNS disease Patients with refractory or recurrent solid tumors or lymphomas, excluding CNS tumors, are eligible; patients must have had histologic verification of malignancy at original diagnosis or relapse; patients with primary CNS tumors, known CNS metastases, or a prior history of CNS metastases are not eligible Patients with prior history of or known metastatic CNS disease involvement are not eligible; (Note: CNS imaging for patients without a known history of CNS disease is only required if clinically indicated) Patients who have a known primary or metastatic CNS tumor at the time of study enrollment are not eligible; a prior history of metastatic CNS tumor is allowed as long as there is no evidence of CNS disease at study enrollment Known active central nervous system (CNS) leukemia or lymphoma – patients with previously treated CNS disease are permitted if neurologically stable with no ongoing or anticipated need for steroid therapy are eligible Patients who have a primary or metastatic CNS tumor at the time of study enrollment are not eligible; a prior history of metastatic CNS tumor is allowed as long as there is no evidence of CNS disease at study enrollment Subjects with the following CNS status are eligible only in the absence of neurologic symptoms suggestive of CNS leukemia, such as cranial nerve palsy: \r\n* CNS 1, defined as absence of blasts in cerebral spinal fluid (CSF) on cytospin preparation, regardless of the number of white blood cells (WBCs); \r\n* CNS 2, defined as presence of < 5/uL WBCs in CSF and cytospin positive for blasts, or > 5/uL WBCs but negative by Steinherz/Bleyer algorithm\r\n* CNS3 with marrow disease who has failed salvage systemic and intensive intrathecally (IT) chemotherapy (and therefore not eligible for radiation)\r\n* Patients with isolated CNS relapse will be eligible if they have previously been treated with cranial radiation (at least 1800 cGy) Active central nervous system (CNS) malignancy as defined by:\r\n* Lymphoma: tumor mass on computed tomography (CT) scan or leptomeningeal disease\r\n* Leukemia: CNS 2 or CNS 3 classification Patients with CNS progression during the trial will be allowed to receive local treatment for CNS metastases and will remain on protocol; trial medications will be held during the time patients are receiving radiation therapy as dictated by their treating physicians Patients with a history of central nervous system (CNS) involvement by lymphoma or with relapsed primary CNS lymphoma will be eligible; patients with active CNS disease are eligible if they have completed a standard treatment for CNS lymphoma and have no evidence of progressive CNS disease at the time of enrollment CNS disease prophylaxis must be stopped > 1 week prior to CTL019 infusion (e.g. intrathecal methotrexate) CNS disease prophylaxis: CNS prophylaxis treatment must be stopped > 1 week prior to CTL019 infusion (e.g. intrathecal methotrexate) Patients with CNS malignancies (primary or metastatic) Known untreated or unstable CNS metastatic disease. Patients with a prior diagnosis of CLL/SLL in central nervous system (CNS) are eligible only if the CNS disease has been treated; patients must be neurologically stable, without progressive symptoms while off of steroids and anti-convulsants; at least 28 days must have elapsed since CNS treatment, and the patient must have recovered from all associated toxicities of treatment; patients who have transfusion-dependent thrombocytopenia or bleeding/coagulation disorders that may increase the risk of life-threatening bleeding are excluded Patients with central nervous system 3 (CNS3) leukemia\r\n* CNS status must be known prior to enrollment; (Note: the CNS status must be determined based on a sample obtained prior to administration of any systemic or intrathecal chemotherapy, except for steroid pretreatment); B-LLy patients with CNS3 disease are not eligible for this protocol or the COG HR ALL protocol; it is recommended that intrathecal cytarabine be administered at the time of the diagnostic lumbar puncture; this is usually done at the time of the diagnostic bone marrow or venous line placement to avoid a second lumbar puncture; this is allowed prior to registration; systemic chemotherapy must begin within 72 hours of the first dose of intrathecal therapy Current or history of CNS lymphoma Symptomatic or untreated central nervous system (CNS) leukemia. Subjects are permitted to enroll if previously treated for CNS disease, free of symptoms at the time of screening, and have not required intrathecal chemotherapy at least 1 month prior to study Day 1. History or evidence of CNS disease. Radiographic screening of all participants without history of CNS metastasis is required. Active CNS lymphoma. Presence of CNS-3 disease and CNS-2 disease with neurological changes Patients must have previously received at least one CNS directed treatment (such as surgery or radiation) OR not be eligible for CNS stereotactic radiosurgery CNS disease: Optional CNS disease expansion cohort: Patients with asymptomatic untreated CNS metastases not needing immediate local therapy or patients with progressive CNS disease following local therapy may be eligible with medical monitor approval. Known history or symptomatic metastatic brain or meningeal tumors (head CT or MRI at screening to confirm the absence of central nervous system [CNS] disease if patient has symptoms suggestive or consistent with CNS disease). Presence of symptomatic CNS lymphoma In cohort 2, eligible patients will include those who have CNS disease that is amenable for surgery (typically < 3 brain metastases and with planned resection by neurosurgery); these patients may include those who have received or not received previous treatment(s) for their CNS Cohort 2: Participants must have progressive disease in CNS or non-CNS sites Patients planning to undergo radiosurgery to any CNS lesion OR patients planning to have surgical resection of ALL of their CNS lesions Symptomatic CNS disease No active CNS disease Patients may have CNS 1, 2 or 3 disease. Patients may have CNS 1 or CNS 2 disease but not CNS 3. Patients with untreated (primary) or symptomatic CNS (primary or metastatic) malignancies; patients with CNS metastases who have undergone surgery or radiotherapy or who have been on a stable dose of corticosteroids for at least 2 weeks and whose disease is stable prior to the first scheduled day of dosing will be eligible for the trial. Patients with metastatic disease i.e. leptomeninges, multi-focal lesions in the CNS CNS metastatic disease Have CNS lesions that are confirmed to be stable or regressing on imaging since the time of the last CNS treatment including the pre-treatment CT or MRI scan for this trial. Patient with active CNS disease. CNS disease unless radiation therapy and/or surgery has been completed and serial evaluation demonstrates stable disease Patient must have relapsed/refractory acute myelogenous leukemia (AML) with ? 5% blast in the bone marrow or biopsy confirmed chloroma. Patient may have CNS 1, 2 or 3 disease. Isolated CNS relapse is not eligible. Patients with CNS 3 disease or symptomatic CNS disease Patients must have histological proof of a cancer - melanoma, breast, or lung cancer - which has spread to the CNS or glioblastoma (GBM) or other primary malignant neoplasm of the CNS which has been treated with standard treatments, which may include radiation, and must be measurable (RECIST). Active ALL in the CNS or testes Medically apparent CNS lymphoma or leptomeningeal disease History of central nervous system (CNS) hemorrhage or thrombosis; patients with a history of CNS lymphomatous involvement are eligible only if their CNS disease is in remission at the time of study entry Symptomatic or untreated central nervous system (CNS) metastatic disease. Patients with previously treated CNS metastatic disease which has been stable for at least 56 days are eligible Symptomatic CNS disease Primary or secondary CNS lymphoma Known primary CNS lymphoma Patients with untreated and/or symptomatic CNS malignancies (primary or metastatic); patients with CNS metastases who have undergone surgery or radiotherapy, whose disease is stable, and who have been on a stable dose of corticosteroids for at least 2 weeks prior to the first scheduled day of dosing will be eligible for the trial Patients with a history of central nervous system (CNS) metastases from cancer are not excluded provided that the metastatic CNS disease has been effectively treated and there is no evidence of active CNS disease as evidence by stable clinical findings and stable radiographic findings for a period of 6 weeks Patients with a history of CNS metastases from cancer are not excluded provided that the metastatic CNS disease has been effectively treated and there is no evidence of active CNS disease as evidenced by stable clinical findings and stable radiographic findings for a period of 6 weeks Patients with a history of CNS metastases from cancer are not excluded provided that the metastatic CNS disease has been effectively treated and there is no evidence of active CNS disease as evidenced by stable clinical findings and stable radiographic findings for a period of 6 weeks (cohort 2) In the absence of rapidly progressing disease, the interval from prior treatment to time of initiation of ponatinib administration will be at least 2 weeks for cytotoxic agents OR at least 5 half-lives for cytotoxic/non-cytotoxic agents; use of one dose of cytarabine (up to 2 g/m^2) or hydroxyurea for patients with rapidly proliferative disease is allowed before the start of study therapy and for the first eight weeks on study therapy from the day of enrollment, either prior to or concomitantly with ponatinib administration initially to control the peripheral blast count; concurrent therapy for central nervous system (CNS) prophylaxis or continuation of therapy for controlled CNS disease is permitted; controlled CNS leukemia is defined by the absence of active clinical signs of CNS disease and no evidence of CNS leukemia on the most recent 2 simultaneous cerebrospinal fluid (CSF) evaluations Patients must have the status of central nervous system (CNS)1 or CNS2 only, and no clinical signs or neurologic symptoms suggestive of CNS leukemia, such as cranial palsy History of CNS hemorrhage within 28 days of study entry. This criterion may be waived at the investigator's request if the CNS hemorrhage was asymptomatic, with approval of the Medical Monitor CNS lesions: A) Patients with CNS parenchymal or meningeal-based lesions that are present at study entry are NOT eligible due to concerns regarding toxicity attribution. B) Who have active CNS disease or a history of cranial irradiation are excluded due to concerns regarding toxicity attribution. Patients with previously treated leptomeningeal disease or brain metastases without evidence of remaining tumor by PET, MRI scan, or spinal fluid will be eligible; however such patients currently taking steroids as prophylaxis against seizures are not eligible. Patients with SCNSL actively receiving treatment for extra-CNS disease are excluded History of central nervous system (CNS) disease, CNS radiation, intrathecal therapy, or CNS surgery Exclusion criteria include previous central nervous system (CNS) radiation or CNS tumors that in the judgment of the investigators are likely to undergo progression during or shortly after radiotherapy Central nervous system disease Patients must not be known to have AML in the central nervous system (CNS) Central nervous system (CNS) status must be determined based on a sample obtained prior to the administration of any systemic or intrathecal chemotherapy, with the exception of steroid pretreatment Patients with central nervous system (CNS) disease are not eligible AML patients with active central nervous system (CNS) disease will be excluded. Active extramedullary AML in testes or central nervous system (CNS) Non-central nervous system (CNS) radiotherapy within 1 week prior to C1D1 of study therapy History or evidence of uncontrollable central nervous system (CNS) disease Participant must not have a known uncontrolled malignancy of the central nervous system. Subject has known current central nervous system (CNS) disease Presence of any active central nervous system (CNS) disease at the time of evaluation (parenchymal or leptomeningeal) Known central nervous system mass lesion Patients with central nervous system involvement by ALL are eligible and may receive concomitant treatment with radiation therapy and/or intrathecal chemotherapy in accordance with standard medical practice; for patients with central nervous system (CNS) disease, dexamethasone may be temporarily administered instead of prednisone to reduce CNS pressure, at the discretion of the treating physician and after discussion with the Memorial Sloan-Kettering (MSK) principal investigator (PI); once dexamethasone is no longer needed, prednisone should be given as per protocol for 28 days Has a history of primary central nervous system malignancy. History of central nervous system (CNS) disease is acceptable if effectively treated and demonstrated stable disease for >= 2 months from protocol tissue procurement Active central nervous system (CNS) disease at time of screening. Participants must be >= 2 weeks since any prior radiation, including central nervous system (CNS) radiation Patients with primary central nervous system (CNS) cancer. Participants must be >= 2 weeks since any prior radiation, including central nervous system (CNS) radiation Active central nervous system (CNS) disease. Central nervous system malignancy Measurable disease according to RECIST v1.1 (must be outside central nervous system (CNS)) Central nervous system (CNS) tumors Central nervous system (CNS) disease Active extramedullary AML in testes or central nervous system (CNS) Patients with retinoblastoma protein (Rb1) positive recurrent, progressive or refractory central nervous system (CNS) tumors Uncontrolled metastatic disease to the brain or central nervous system (CNS). Without clinical signs of active central nervous system disease Presence of central nervous system (CNS) disease, which is symptomatic TREATMENT WITH SJCAR19: Central nervous system (CNS)-3 disease with or without neurologic changes Patients must not have evidence of active central nervous system (CNS) disease Evidence of > grade 1 central nervous system (CNS) hemorrhage on the baseline MRI scan. Recurrent or refractory ALL limited to isolated testicular or isolated central nervous system (CNS) disease Primary central nervous system malignancy Active central nervous system (CNS) or extramedullary disease Known central nervous system malignancy. Note: Central nervous system imaging is only required in subjects with suspected central nervous system malignancy. Patients have a histologically or radiographically confirmed relapsed or refractory solid tumor or primary central nervous system (CNS) malignancy Subjects with symptomatic central nervous system (CNS) disease which is not adequately controlled Uncontrolled central nervous system (CNS) disease (for hematologic malignancies) Have central nervous system disease (CNS) as follows: Active central nervous system (CNS) disease Known primary central nervous system (CNS) malignancy Patients with a history of central nervous system disease must have no clinical or radiological evidence of central nervous system (CNS) disease at the time of protocol enrollment and with CNS toxicity =< grade 2; patients with seizure disorders may be enrolled if seizures are well controlled Presence of active and clinically relevant central nervous system (CNS) disorder; Presence of active and clinically relevant Central Nervous System (CNS) disorder (Bevacizumab-related exclusion) History or evidence upon physical/neurological examination of central nervous system (CNS) disease (e.g. seizures) unrelated to cancer unless adequately treated with standard medical therapy Active central nervous system (CNS) disorder or seizure disorder or known CNS disease or neurologic symptomatology Presence of any significant central nervous system (CNS) or psychiatric disorder(s) that would hamper the patient's compliance; Active central nervous system (CNS) disease in patient with history of CNS malignancy. Active central nervous system (CNS) or extramedullary disease unless approved by the principal investigator (PI) Active central nervous system malignancy Rapidly progressive, clinically unstable central nervous system hematological malignancy. Note: Central nervous system evaluation is only required in subjects with known or suspected central nervous system malignancy. Active, uncontrolled central nervous system (CNS) disease Active central nervous system (CNS) malignancy Eligible for extra-central nervous system (CNS) SAbR to 1-6 sites of disease Active central nervous system (CNS) disease in patient with history of CNS malignancy Active central nervous system malignancy Patients with clinical evidences of active central nervous system (CNS) disease at inclusion Active central nervous system (CNS) disease Suspected AML-related central nervous system involvement; a lumbar puncture (LP) is not required to exclude central nervous system (CNS) disease Presence of any central nervous system tumor that has not been stable for at least 4 weeks off corticosteroids. Patient with active central nervous system (CNS) disease AND (by central assessment) either: Patients with central nervous system disease are eligible for enrollment if they have received prior radiotherapy or surgery to sites of CNS (central nervous system) metastatic disease and are without evidence of clinical progression for at least 12 weeks after therapy Participant has overt central nervous system (CNS) disease (CNS 3 status) Patients with a history of central nervous system disease must not have severe peripheral neuropathy, signs of leukencephalopathy, or active central nervous system (CNS) infection; patients with seizure disorders may be enrolled if seizures are well controlled on anticonvulsant therapy Stable central nervous system (CNS) disease that has been adequately treated and is not under active treatment allowed Patients with active central nervous system (CNS) or epidural tumor Patients with central nervous system (CNS) disease who have received treatment and disease has been stable for four weeks are eligible Active central nervous system (CNS) or extramedullary disease Active central nervous system (CNS) disease. Patients with central nervous system (CNS) tumors who are receiving steroids are eligible Non-central nervous system (CNS) radiotherapy within 1 week prior to C1D1 of study therapy Significant co-morbid central nervous system disease, including but not limited to, multiple sclerosis No active central nervous system (CNS) disease Patients with active central nervous system (CNS) disease Patients may NOT have evidence or symptoms of central nervous system (CNS) disease at the time of enrollment Known chronic or active viral infections of the central nervous system (CNS) Confirmed absence of central nervous system (CNS) disease Active central nervous system (CNS) disease Patients with active central nervous system (CNS) disease Prior history of encephalitis, multiple sclerosis, or other central nervous system (CNS) infection No uncontrolled seizure disorder, active neurological disease, or known central nervous system (CNS) disease Patients with active central nervous system (CNS) or epidural tumor Patients with known malignant disease of the central nervous system. History of primary central nervous system (CNS) disease that would interfere with subject evaluation Patient with active central nervous system (CNS) disease Patient has a primary central nervous system tumor Central nervous system (CNS) tumor refractory to intrathecal chemotherapy and/or cranio-spinal radiation No current central nervous system (CNS) myeloma at time of enrollment Tumors arising outside of the central nervous system (CNS) Any history of disease involving the central nervous system (Part 1). Known active disease involving the central nervous system (Part 2). Presence of central nervous system (CNS) disease Stable central nervous system (CNS) disease that has been adequately treated and is not under active treatment allowed Active central nervous system malignancy Many patients present with concomitant systemic disease outside of the central nervous system; extra-central nervous system (CNS) disease status should meet the following criteria:\r\n* Patients with concomitant systemic disease under control with current or prior systemic treatment, as per primary treating physician\r\n* Patients without any evidence of systemic disease, either receiving systemic treatment or on active observation (Cohort D) Active central nervous system malignancy Patients may have active malignancy outside the central nervous system Subjects with rapidly progressing central nervous system (CNS) disease with associated neurological deterioration Patients with central nervous system (CNS) malignancies. Active central nervous system malignancy Patients with limited disease (if MF/SS: stages IA) or central nervous system (CNS) disease. Active central nervous system (CNS) disease in patient with history of CNS malignancy Concommitant therapy that includes other chemotherapy that is or may be active against ALL (except central nervous system [CNS] therapy) Active central nervous system (CNS) disease Active leukemic central nervous system (CNS) disease Eligible for extra-central nervous system (CNS) SABR to 1-5 sites of disease Central nervous system (CNS) toxicity including peripheral neuropathy =< grade 2 Subject has known current central nervous system (CNS) disease Pre-existing central nervous system (CNS) demyelination or seizure disorders Central nervous system (CNS) toxicity =< grade 2 Patients with active central nervous system (CNS) malignancy Symptomatic leukoencephalopathy, active central nervous system (CNS) malignancy or other neuropsychiatric abnormalities believed to preclude transplantation (previous CNS malignancy, presently in complete remission [CR] is not an exclusion) Patient has chronic or active viral infections of the central nervous system (CNS) Patients with disease progression in the central nervous system (CNS) only Patients with active central nervous system disease or with granulocytic sarcoma as sole site of disease Patients with active central nervous system (CNS) or epidural tumor History of central nervous system (CNS) disease Central nervous system disease as evidence by clinical symptomatology Subjects with known central nervous system disease Primary disease involving the Central Nervous System (CNS) Patients with central nervous system disease are eligible for enrollment if they have received prior radiotherapy or surgery to sites of central nervous system metastatic disease, have been off glucocorticoids for at least 4 weeks, have no overt evidence of neurological deficit and are ? 6 weeks from completion of brain irradiation. Active central nervous system disease. Symptomatic leukoencephalopathy, active central nervous system (CNS) malignancy or other neuropsychiatric abnormalities believed to preclude transplantation Participants with known central nervous system disease History of or active central nervous system (CNS) malignancy Active/symptoms of central nervous system (CNS) disease Evidence for central nervous system (CNS) metastatic disease History or evidence upon physical/neurological examination of central nervous system (CNS) disease unrelated to cancer, unless adequately treated with standard medical therapy (e.g. uncontrolled seizures) Patient has active or history of central nervous system (CNS) disease Adequate central nervous system function defined as:\r\n* Patients with a history of central nervous system (CNS) disease must have no clinical or radiological evidence of CNS disease at the time of study enrollment\r\n* Patients with seizure disorders may be enrolled if seizures are well controlled on anticonvulsants\r\n* CNS toxicity =< grade 2 Active central nervous system (CNS) disease at the time of treatment Active central nervous system (CNS) or symptomatic epidural metastatic disease History of central nervous system (CNS) lymphoma or other CNS disease Known cytopathologically confirmed central nervous system (CNS) infiltration Current central nervous systemic disease No active central nervous system (CNS) disease Subjects with active cancer that has spread to the central nervous system Known central nervous system (CNS) disease Patients with known active central nervous system (CNS) disease History of central nervous system (CNS) thrombotic/embolic or ischemic event(s) Symptomatic central nervous system (CNS) disease. Known active central nervous system (CNS) malignancy Known cytopathologically confirmed central nervous system (CNS) infiltration Significant co-morbid central nervous system disease, including but not limited to, multiple sclerosis Hematologic and primary central nervous system (CNS) malignancies Any primary or active central nervous system (CNS) malignancy, including metastatic disease Central nervous system function defined as not severely somnolent or comatose (central cortical neurotoxicity scale < grade 3) Presence of central nervous system (CNS) metastatic disease History of demyelinating disease or inflammatory disease of the central nervous system or the peripheral nervous system Pathology from the resected brain metastasis must be consistent with a non-central nervous system primary site; Note: patients with or without active disease outside the nervous system are eligible (including patients with unknown primaries), as long as the pathology from the brain is consistent with a non-central nervous system primary site Active central nervous system (CNS) disease Patients with stable, treated central nervous system (CNS) disease are eligible Have active Central Nervous System (CNS) disease Patients with relapse also detected in the central nervous system (CNS) may be treated on this protocol; however, if intrathecal chemotherapy is being administered, T cells should not be administered until at least 24 hours thereafter Active central nervous system (CNS) disease in patient with history of CNS malignancy History or clinically suspicious for cancer-related Central Nervous System disease Patients may have active malignancy outside the central nervous system Central Nervous System (CNS) disease only. Known central nervous system malignancy. Active central nervous system (CNS) disease Active central nervous system (CNS) or extramedullary malignant disease Patients with central nervous system (CNS) disease or testicular disease are eligible Active central nervous system disease (CNS) metastases, as indicated by clinical symptoms, cerebral edema or progressive growth Uncontrolled central nervous system (CNS) disease Known central nervous system (CNS) disease Patients with active central nervous system (CNS) malignancy are not eligible for this trial Active/symptoms of central nervous system (CNS) disease Central nervous system (CNS) disease Primary brain or other central nervous system malignancy. History of central nervous system hemorrhage Active central nervous system (CNS) disease in patient with history of CNS malignancy Patients with documented central nervous system (CNS) disease Severe central nervous system, pulmonary, or renal disease not related to the participant's cancer. Has a history of primary central nervous system malignancy. Patient has no worsening central nervous system symptoms; and Patients with active central nervous system (CNS) disease Known central nervous system disease (e.g., Alzheimer's disease). Patients with a history of central nervous system (CNS) malignancy. Patients with central nervous system disease Has a symptomatic central nervous system (CNS) tumor causing nausea and/or vomiting Patient has active or history of central nervous system (CNS) disease. History of central nervous system (CNS) PTLD Active Central Nervous System [CNS] disease Active central nervous system (CNS) disease b. Central nervous system (CNS) trauma or active seizure disorders requiring medication Primary malignancy of the central nervous system. Patients with active central nervous system (CNS) disease Central nervous system tumors are allowed Patients with documented central nervous system (CNS) ischemia and/or infarction, whether symptomatic or discovered incidentally without clinical symptoms, will be excluded from study participation Active MM involving the central nervous system. Pre-existing central nervous system (CNS) demyelination or seizure disorders Active MM involving the central nervous system (CNS). Active central nervous system lesions Active central nervous system (CNS) disease (related to primary malignancy) at the time of enrollment History of significant central nervous system (CNS) injury or disease predating or unrelated to cancer diagnosis Patient has symptomatic primary or metastatic central nervous system (CNS) disease Patients with active central nervous system (CNS) disease, such as clinically-evident metastases or leptomeningeal disease, dementia, or encephalopathy Patients with history of seizures or uncontrolled central nervous system (CNS) disease, significant hepatic or renal dysfunction Patients with active central nervous system (CNS) disease, such as clinically-evident metastases or leptomeningeal disease, dementia, or encephalopathy. Comorbidities at particular risk (i.e., active central nervous system [CNS], active CNS metastases, hydrocephalus or coagulopathy) History of central nervous system (CNS) tumor Cranial radiotherapy for central nervous system (CNS) leukostasis; History of Grade >= 2 central nervous system (CNS) hemorrhage All patients need to have received at least one prior central nervous system (CNS) directed therapy; there is no restriction on the number of recurrences Participant is currently receiving treatment with benzodiazepines or other central nervous system (CNS) depressants Active central nervous system (CNS) disease Active central nervous system (CNS) disease (the action for acupuncture may be associated with central nervous system activity, and patients with CNS pathology may respond differently to treatment than the general population) Uncontrolled central nervous system (CNS) disease (for hematologic malignancies) Active central nervous system malignancy Non-central nervous system (CNS) malignant disease must be sufficiently controlled so that patient can be without additional systemic therapy for approximately 2 months Subjects with known central nervous system disease Has a symptomatic primary or metastatic central nervous system (CNS) malignancy with nausea and/or vomiting (asymptomatic participants may participate in study) Central nervous system (CNS) only disease on recent imaging MM involving the central nervous system. Diagnosis: Must have MRI documenting a measurable lesion w/in central nervous system consistent with primary central nervous system tumor, for which maximal safe surgical resection is indicated Suspected central nervous system (CNS) tumor(s) or sarcoma. Uncontrolled Disseminated Intravascular Coagulation (DIC) Subject has clinical evidence of Disseminated Intravascular Coagulation Have evidence of uncontrolled disseminated intravascular coagulation Patients must have no clinical evidence of central nervous system (CNS) or pulmonary leukostasis, disseminated intravascular coagulation, or CNS leukemia Immediate life-threatening, severe complications of leukemia such as uncontrolled bleeding, pneumonia with hypoxia or shock, and/or disseminated intravascular coagulation FOR AML ONLY: Absence of uncompensated disseminated intravascular coagulation (DIC- as diagnosed by standard International Society on Thrombosis and Hemostasis [ISTH] criteria) AML ONLY: Current disseminated intravascular coagulopathy (DIC) Has an active bleeding disorders or evidence of chronic or acute disseminated intravascular coagulation (DIC) Patients must have no clinical evidence of central nervous system (CNS) or pulmonary leukostasis, disseminated intravascular coagulation, or CNS leukemia Have evidence of uncontrolled disseminated intravascular coagulation Clinically significant coagulation abnormality, such as disseminated intravascular coagulation. Have immediate, life-threatening, severe complications of leukemia, such as uncontrolled bleeding, pneumonia with hypoxia or sepsis, and/or disseminated intravascular coagulation. Disseminated intravascular coagulopathy with active bleeding or signs of thrombosis Subject has clinical evidence of Disseminated Intravascular Coagulation (DIC) Subject has clinically significant abnormality of coagulation profile, such as disseminated intravascular coagulation (DIC). Clinically significant coagulation abnormality, such as disseminated intravascular coagulation. Subjects with immediately life-threatening, severe complications of leukemia such as uncontrolled bleeding, pneumonia with hypoxia or shock, and/or disseminated intravascular coagulation. Has clinical evidence of central nervous system (CNS) or pulmonary leukostasis, disseminated intravascular coagulation, or CNS multiple myeloma Subjects who have had clinical evidence of central nervous system (CNS) or pulmonary leukostasis, disseminated intravascular coagulation, or CNS multiple myeloma, or plasma cell leukemia Subjects who have had clinical evidence of central nervous system (CNS) or pulmonary leukostasis, disseminated intravascular coagulation, or CNS leukemia. Has clinical evidence of central nervous system (CNS) or pulmonary leukostasis, disseminated intravascular coagulation, or CNS multiple myeloma Has acute promyelocytic leukemia, clinically uncontrolled disseminated intravascular coagulation, or peripheral cytopenia Hereditary or acquired coagulopathies (e.g., hemophilia, von Willebrand disease, or cancer associated disseminated intravascular coagulation [DIC]) History of bleeding (i.e. disseminated intravascular coagulation or clotting factor deficiency); Subject has disseminated intravascular coagulation abnormality (DIC). Subjects with immediately life-threatening, severe complications of leukemia such as uncontrolled bleeding, pneumonia with hypoxia or shock, and/or disseminated intravascular coagulation. Uncontrolled disseminated intravascular coagulation. Absence of coagulopathy (no uncompensated disseminated intravascular coagulation, DIC) at screening Clinical picture indicative of leukostasis or evidence of disseminated intravascular coagulopathy Patients with laboratory findings consistent with grade equal to greater than 3 disseminated intravascular coagulation (DIC) or any grade 2 DIC that does not correct Active bleeding disorders or evidence of evidence of chronic or acute disseminated intravascular coagulation (DIC) Subject has disseminated intravascular coagulation abnormality (DIC) Patients must have no clinical evidence of central nervous system (CNS) or pulmonary leukostasis, disseminated intravascular coagulation, or CNS leukemia Serious concurrent medical problems, uncontrolled infections, or disseminated intravascular coagulopathy (DIC), hepatic cirrhosis, or chronic kidney disease. Disseminated intravascular coagulation History of known bleeding disorder (i.e. disseminated intravascular coagulation or clotting factor deficiency); Evidence of disseminated intravascular anticoagulation (DIC) as determined by the patient’s primary provider Coagulopathies including disseminated intravascular coagulation (DIC), receiving anticoagulant or antiplatelet agents Known diagnosis of disseminated intravascular coagulation (DIC) Known diagnosis of disseminated intravascular coagulation Presence of central nervous system (CNS) involvement requiring active treatment Leukemia with active central nervous system (CNS) involvement Active central nervous system (CNS) involvement by leukemia Known active central nervous system (CNS) involvement by lymphoma, including parenchymal and/or lymphomatous meningitis Active, uncontrolled central nervous system (CNS) involvement by lymphoma Patients with known active central nervous system (CNS) involvement by lymphoma, including leptomeningeal involvement Known active central nervous system (CNS) involvement by lymphoma should be excluded from this clinical trial Active central nervous system (CNS) involvement with leukemia Active, uncontrolled central nervous system (CNS) leukemia involvement Subject has known active central nervous system (CNS) involvement from AML Active central nervous system (CNS) involvement by lymphoma, including untreated symptomatic epidural disease Patients with active central nervous system (CNS) involvement with lymphoma are not eligible Participant has known active central nervous system (CNS) involvement with AML. Patients with known active central nervous system (CNS) disease, including leptomeningeal involvement Active central nervous system (CNS) involvement by malignancy Active central nervous system (CNS) metastases and/or leptomeningeal involvement Known active central nervous system (CNS) involvement Known active central nervous system (CNS) involvement by MM Subject has known active central nervous system (CNS) involvement with AML Evidence of active central nervous system (CNS) involvement known active central nervous system (CNS) involvement by malignancy. Active central nervous system (CNS) or testicular involvement by leukemia No active central nervous system (CNS) metastatic disease. NOTE: Subjects with CNS involvement must meet ALL of the following to be eligible: History of or known active central nervous system (CNS) involvement with AML Active central nervous system (CNS) involvement or leptomeningeal involvement Patients with known active central nervous system (CNS) disease, including leptomeningeal involvement Active, untreated central nervous system (CNS) involvement Active central nervous system (CNS)-only involvement by malignancy (note: participants with secondary CNS involvement are allowed on study) Patients with active central nervous system (CNS) involvement with lymphoma are not eligible History of or active central nervous system (CNS) or peripheral nerve stimulation (PNS) involvement Has known clinically active central nervous system (CNS) involvement Active central nervous system (CNS) involvement within the previous 2 months Active central nervous system (CNS) involvement of the underlying malignancy Active central nervous system (CNS) neoplastic involvement Known active central nervous system (CNS) involvement Patient with active central nervous system (CNS) involvement Patients with active central nervous system (CNS) involvement by malignant cells History of or known active central nervous system (CNS) involvement or leptomeningeal involvement Active central nervous system (CNS) involvement or leptomeningeal metastases involvement Known active central nervous system (CNS) involvement with AML at study entry Has known clinically active central nervous system (CNS) involvement OR history of resolved CNS involvement by multiple myeloma Patients with history of central nervous system (CNS) involvement or active CNS involvement by malignancy Active central nervous system (CNS) involvement by malignancy Active Central Nervous System (CNS) involvement by malignancy Has known clinically active central nervous system (CNS) involvement Have active leukemic involvement of the central nervous system (CNS). Active central nervous system (CNS) involvement of disease Active AML involvement of the central nervous system (CNS) with disease refractory to intrathecal chemotherapy AML patients with known, active leptomeningeal/central nervous system (CNS) involvement No active extramedullary leukemia or known active central nervous system (CNS) involvement by malignancy; such disease treated into remission is permitted Active central nervous system (CNS) involvement with leukemia Participant has known active central nervous system (CNS) involvement with AML. Any past or current Central Nervous System (CNS) involvement, including leptomeningeal leukemia. Patients with active central nervous system (CNS) involvement with lymphoma should be excluded from this clinical trial Patient with active central nervous system (CNS) involvement with lymphoid malignancy Active diagnosis of central nervous system (CNS) involvement with CLL Active central nervous system (CNS) disease involvement Clinically active central nervous system (CNS) cancer involvement. Imaging to exclude CNS involvement not required. Known active cerebral/meningeal involvement with lymphoma; asymptomatic patients with previously treated and resolved central nervous system (CNS) lymphoma involvement are permitted Had evidence of active central nervous system (CNS) involvement Active central nervous system (CNS) lymphoma/leukemia - Patients with prior CNS involvement are eligible provided that it has been treated and is in remission Active or symptomatic central nervous system (CNS) disease or epidural involvement Active involvement of the Central Nervous System (CNS). Active central nervous system (CNS) involvement of their malignancy. No active extramedullary leukemia or known active central nervous system (CNS) involvement by malignancy; such disease treated into remission is permitted Active central nervous system (CNS) involvement by malignancy No active extramedullary leukemia or known active central nervous system (CNS) involvement by malignancy; such disease treated into remission is permitted Patient must not have active central nervous system (CNS) involvement Active central nervous system (CNS) involvement by malignant cells EXCLUSION CRITERIA FOR ENROLLMENT (PRE-TRANSPLANT): Active involvement of the central nervous system with malignancy (previous central nervous system [CNS] involvement is allowed if clearance of CNS disease has been documented prior to enrollment) Active central nervous system (CNS) involvement by malignant cells Active central nervous system (CNS) involvement by malignant cells Active central nervous system (CNS) involvement by malignant cells Clinical suspicion of active central nervous system (CNS) involvement by leukemia