Prior history of allogeneic stem cell transplantation Has a history of having undergone allogeneic stem cell transplantation, or any other allogeneic or xenogeneic transplant Prior allogeneic stem-cell transplantation (SCT) Patients with history of allogeneic stem cell transplantation Patients are considered to have failed available therapies or to be ineligible for or to not be interested in intensive chemotherapies, including allogeneic hematopoietic stem cell transplantation Has undergone prior allogeneic hematopoietic stem cell transplantation within the last 5 years. Has ever received or is scheduled to receive an Allogeneic Hematopoietic Stem Cell Transplantation (alloHSCT) Has failed to respond to, relapsed following, not eligible for, or opted not to participate in allogeneic stem cell transplantation Suitable candidate to receive allogeneic stem cell transplantation; patient is eligible for study if a suitable candidate refuses to undergo an allogeneic stem cell transplant or a suitable donor cannot be found Patients who are candidates for allogeneic stem cell transplantation. Patients who have had an allogeneic hematopoietic stem cell transplantation are not eligible. Has undergone prior allogenic hematopoietic stem cell transplantation. Prior allogenic hematopoietic stem cell transplantation. Relapsed patients who have undergone autologous or allogeneic hematopoietic stem cell transplantation previously Patients with psychological or medical condition that patient's physician deems unacceptable to proceed to allogeneic hematopoietic stem cell transplantation Prior allogeneic stem cell transplantation Prior autologous or allogeneic stem cell transplantation Relapse after allogeneic stem cell transplantation prior to post-transplant day 30 Is eligible for intensive chemotherapy and/or allogeneic stem cell transplantation. The reason a participant is not eligible for intensive chemotherapy and/or allogeneic stem cell transplantation may consist of one or more of the following factors: Has a history of allogeneic stem cell transplantation Subjects who have opted not to undergo allogeneic hematopoietic stem cell transplantation and who are not deemed eligible for high intensity chemotherapy. Prior history of allogeneic hematopoietic stem cell transplantation. Has a history of allogeneic stem cell transplantation Prior stem cell transplantation for myeloma Prior history of stem cell transplantation Prior allogeneic stem cell transplantation (ASCT) or other anti-CD22 immunotherapy within =< 4 months before first dose of study treatment Prior autologous or allogeneic stem cell transplantation Must have undergone allogeneic hematopoietic stem cell transplantation (HSCT) (regardless of stem cell source) Prior stem cell transplantation Autologous stem cell transplantation within 12 weeks before the starting IP treatment or past history of allogeneic stem cell transplantation. Has undergone prior allogeneic hematopoietic stem cell transplantation within the last 5 years Previous allogeneic hematopoietic stem cell transplantation Have undergone allogeneic stem cell transplantation No plan for allogeneic stem cell transplantation within 3 months Patients who have undergone allogeneic stem cell transplantation and have required systemic treatment for GVHD (including but not limited to oral or parenteral corticosteroids, ibrutinib, and extracorporeal phototherapy) within the last 12 weeks Prior hematopoietic allogenic stem cell transplantation. Subjects must not have undergone allogeneic stem cell transplantation Prior treatment with allogeneic stem cell transplantation Has undergone prior allogeneic hematopoetic stem cell transplantation within the last 5 years Patients who have undergone allogeneic stem cell transplantation Patients who have undergone prior autologous stem cell transplantation or allogeneic transplantation Allogeneic stem cell transplantation within 6 months, or has active GVHD requiring ongoing immunosuppression. Prior allogeneic stem cell transplantation Patients with psychological or medical condition that patient's physician deems unacceptable to proceed to allogeneic hematopoietic stem cell transplantation Prior allogeneic marrow or stem cell transplantation. Malignant conditions for which CD34+ selected, T-cell depleted allogeneic hematopoietic stem cell transplantation is indicated such as: Patients eligible for hematopoietic stem cell transplantation Patients who have received prior allogeneic stem cell-transplantation Patients who have undergone a stem cell transplantation. Patients who have had a prior stem cell transplantation are NOT eligible for participation Prior allogeneic hematopoietic stem cell transplantation within previous 100 days Stem cell transplantation Patients who have received allogeneic hematopoietic stem cell transplantation are ineligible Previous stem cell collection or transplantation (autologous or allogeneic) History of allogeneic stem cell transplantation Prior allogeneic stem cell transplantation Patients will have completed induction therapy, achieved 1st CR and will have completed any planned post-remission therapy; patients are not candidates for allogeneic stem cell transplantation; for purposes of this study, patients who are not candidates for allogeneic stem cell transplantation shall be defined as 1) those who do not meet the eligibility criteria of an open allogeneic transplant protocol or 2) those who do not have a suitable available human leukocyte antigen (HLA) matched donor available or 3) those who refuse to undergo stem cell transplantation or 4) those patients whose disease is characterized by \good risk\ features (for AML the following cytogenetic subtypes: t(8;21), inv(16), or t(16;16), t(15;17), normal karyotype with mutated nucleophosmin (NPM1) and negative for tandem duplication of fms-related tyrosine kinase 3 (FLT-3); for ALL: T cell phenotype of any B lineage disease exclusive of t(9;22) or t(4;11) in whom allogenic stem cell transplantation in 1st CR would not be offered as standard of care\r\n* Alternatively, those patients greater than or equal to 60 years of age who have achieved 1st CR and in whom no further postremission chemotherapy is planned may be enrolled Patients who have undergone autologous or allogeneic stem cell transplantation Prior allogeneic stem cell transplantation Prior allogeneic stem cell transplantation (SCT) within the last 5 years. Has undergone prior allogeneic hematopoetic stem cell transplantation within the last 5 years. Allogeneic hematopoietic stem cell transplantation within the last 5 years. Prior allogeneic stem-cell transplantation is excluded. Patients deemed clinically eligible for allogeneic stem cell transplantation. Hematopoietic stem cell transplantation ? 4 months of dosing Inability to comply with the requirements for care after allogeneic stem cell transplantation Patients must NOT have received autologous or allogeneic stem cell transplantation Prior allogeneic stem-cell transplantation (SCT) have undergone previous allogenic stem cell transplantation Prior allogeneic stem cell transplantation (SCT) Has received more than 1 hematopoietic stem cell transplantation. Eligible for allogenic stem cell transplantation. Prior allogeneic stem cell transplantation Patients that have received prior allogeneic stem cell transplantation are excluded from this study Prior stem cell transplantation allogeneic or autologous AML participants < 60 years old must be in second or further relapse or relapsing after allogeneic stem cell transplantation regardless of number of relapses Prior treatment with stem cell transplantation Prior stem cell transplantation (autologous or allogeneic) Prior allogeneic hematopoietic stem cell transplantation Prior hematopoietic stem cell transplantation Allogeneic stem cell transplantation Prior allogeneic stem cell transplantation Recipients of prior allogeneic hematopoietic stem cell transplantation Previous allogenic stem cell transplantation. Patients must be between 100 - 200 days after allogeneic stem cell transplantation Patient who has undergone allogeneic stem cell transplantation Day > 100 after allogeneic hematopoietic stem cell transplantation Patients who have undergone prior allogeneic hematopoietic stem cell transplantation History of allogeneic stem cell transplantation Patients who have undergone autologous/allogeneic stem cell transplantation are eligible Previous hematopoetic stem cell transplantation. Patients must meet institutional criteria for eligibility for non-myeloablative allogeneic stem cell transplantation There are no liver function test criteria for non-myeloablative allogeneic stem cell transplantation Subjects with hematologic malignancies for whom allogeneic stem cell transplantation is deemed clinically appropriate. At the time of registration, stem cell transplantation is not planned within the next 3 months Prior allogeneic hematopoietic stem cell transplantation (allogeneic stem cell transplant) Previous allogeneic stem-cell transplantation Less than 1 month since completion of autologous stem cell transplantation or less than 3 months since completion of allogeneic stem cell transplantation Prior history allogeneic stem cell transplantation History of allogeneic stem cell transplantation History of allogeneic stem cell transplantation Prior allogeneic stem cell transplantation Prior autologous or allogeneic stem cell transplantation Not eligible for an allogeneic hematopoietic stem cell transplantation Relapse after allogeneic stem cell transplantation prior to post-transplant day 30 Not a candidate for allogeneic stem cell transplantation Patients who have received allogeneic stem cell transplantation < 12 months prior to entering the study Allogeneic stem cell transplantation Previous autologous or allogeneic stem cell transplantation. Prior allogeneic stem cell transplantation. Previous allogeneic stem cell transplantation at any time OR autologous stem cell transplantation within 6 months of study entry. Previous allogeneic stem cell transplantation. The patient has received, or is receiving, allogeneic Stem Cell Transplantation (SCT). Prior allogeneic marrow or stem cell transplantation Any patient undergoing allogeneic hematopoietic stem cell transplantation (either 1st or subsequent) Patients who have undergone a prior allogeneic or autologous stem cell transplantation within the previous six months Not eligible for stem cell transplantation Stem cell transplantation within preceding 60 days prior to registration Previous allogeneic hematopoietic stem cell transplantation Subject underwent allogeneic stem cell transplantation at least 6 months prior to enrollment Patients who have undergone either ablative or non-myeloablative allogeneic stem cell transplantation are eligible Patients must otherwise fulfill institutional criteria for eligibility to undergo myeloablative allogeneic stem cell transplantation Patients who have undergone allogeneic stem cell transplantation for the treatment of any hematological malignancy are eligible Prior allogeneic hematopoietic stem cell transplantation Patients who have had stem-cell transplantation Prior stem cell transplantation Prior autologous stem cell transplantation < 1 month or allogeneic stem cell transplantation < 4 months prior to C1D1. Patients must not have had prior stem cell transplantation (autologous or allogeneic) Patients with history of allogeneic stem cell transplantation History of allogeneic stem cell transplantation Patient must be deemed eligible to proceed with high-dose chemotherapy and autologous stem cell transplantation by local transplant center At least 6 weeks from autologous stem cell transplantation Must be ineligible for high dose therapy/ stem cell transplantation Participants may not be receiving any other non-Food and Drug Administration (FDA) approved study agents at the start of conditioning for stem cell transplantation; patients may receive non-FDA approved agents at the time of screening/enrollment as long as such agent(s) will be discontinued by the start of conditioning for transplantation Eligible for Autologous Hematopoietic stem cell transplantation according at the investigator discretion. B-cell lymphoma classified as either of the following: R/R FL after treatment with at least one prior chemoimmunotherapy regimen that included an anti-cluster of differentiation 20 (CD20) monoclonal antibody; R/R DLBCL after treatment with at least one prior chemoimmunotherapy regimen that included an anti-CD20 monoclonal antibody in participants who are not eligible for second line combination chemotherapy and autologous stem-cell transplantation, have failed second line combination chemotherapy, or experienced disease progression following autologous stem-cell transplantation Patients who completed single autologous stem cell transplant after completion of at most 2 induction regimens (excluding dexamethasone alone) and are in at least stable disease compared to pre-induction in the first 100 days after stem cell transplantation For rituximab in combination with polatuzumab vedotin and lenalidomide (R + Pola + Len) treatment group: R/R DLBCL after treatment with at least one prior chemoimmunotherapy regimen that included an anti-CD20 monoclonal antibody in patients who are not eligible for autologous stem-cell transplantation or who have experienced disease progression following treatment with high-dose chemotherapy plus autologous stem-cell transplantation Previous hematopoietic stem cell transplantation; patients can have had prior relapsed disease as long as they have never been previously transplanted Institutional criteria for and have institutional approval to undergo autologous peripheral blood stem cell transplantation NOTE: There is no limit to the prior number of chemotherapy regimens; patients with prior autologous or allogeneic stem cell transplantation, as well as prior therapy with cyclophosphamide or alemtuzumab, are eligible Patients who have ever received an Autologous Hematopoietic Stem Cell Transplantation (autoHSCT) ARE eligible. Patients who are scheduled to receive an Autologous Hematopoietic Stem Cell Transplantation (autoHSCT) are NOT eligible Recipients of prior autologous hematopoietic stem cell transplantation are ineligible if disease recurrence occurred less than 6 months from their autologous stem cell transplant. Hematological malignancy has been previously treated, has relapsed after or progressed during prior therapy, and has limited potential for benefit from currently available therapy including hematopoietic stem cell transplantation. Other high-risk hematologic malignancies eligible for stem cell transplantation per institutional standard One or more prior lines of chemoimmunotherapy and/or monotherapy with rituximab or other anti-cluster of differentiation (CD)20 antibody; patients may have had a prior autologous stem cell transplant but not prior allogeneic stem cell transplantation Patient has an appropriate donor identified for hematopoietic stem cell transplantation Deemed eligible for autologous stem cell transplantation (ASCT) by standard institutional criteria For ALL: patients must belong to one of the following ‘high risk’ categories: \r\n* Primary refractory as defined by failure to achieve CR after induction and at least one salvage therapy \r\n* Second or subsequent relapse \r\n* Relapse after allogeneic or autologous stem cell transplantation (requirement for second relapse does not apply post-transplant) \r\n* All variants of ALL including T-ALL, B / myeloid, lymphoblastic leukemia lymphoma are eligible Cohort #1: considered eligible for high-dose chemotherapy followed by autologous stem cell transplantation (ASCT) High-dose chemotherapy followed by stem cell transplantation (autologous or allogeneic). Patients with histologically-confirmed symptomatic multiple myeloma or AL amyloidosis undergoing autologous hematopoietic cell transplantation (HCT) with melphalan 140 or 200 mg/m^2 Patients with prior salvage chemo-immunotherapy, radiation therapy, autologous transplantation are included High dose chemotherapy followed by autologous stem cell transplantation within 90 days prior to initiating study treatment; Patients who are candidate for an autologous or allogeneic stem cell transplantation (SCT) will be allowed to receive the study drugs as a “bridge” to transplantation if candidates for transplant Patients with HL or DLBCL must refuse or not be candidates for curative autologous stem cell transplantation Received prior autologous stem cell transplantation as first line therapy for multiple myeloma with subsequent disease relapse/progression Refractory to or intolerant of lenalidomide maintenance following first autologous stem cell transplantation; refractory is defined as disease relapse/progression on therapy or within 60 days of completing therapy; intolerance is defined as the inability to administer >= 10 mg per day due to toxicity Candidate for second autologous stem cell transplantation per local institution’s guidelines with at least 2 x 10^6/kg CD34+ autologous stem cells available for transplantation Prior treatment with chimeric antigen receptor (CAR) T cells or other forms of adoptive cellular therapy, with the exception of autologous stem cell transplantation History of prior autologous hematopoietic cell transplantation Hematological malignancy has been previously treated, has relapsed after or progressed during prior therapy, and has limited potential for benefit from currently available therapy, including hematopoietic stem cell transplantation. Patient participants who have undergone autologous stem cell transplantation (autoSCT) are eligible provided that they are >= 4 weeks from stem cell infusion Patients are planned for treatment with high dose melphalan and autologous hematopoietic cell transplantation (HCT) Autologous stem cell transplantation within 12 weeks prior to study entry RESEARCH SAMPLE COLLECTION: Considered for high-dose melphalan followed by autologous hematopoietic cell transplantation and undergoing pre-HCT workup Diagnosis of multiple myeloma undergoing planned autologous stem cell transplantation Patients must have undergone hematopoietic stem cell transplantation and have moderate to severe chronic GVHD as defined by the National Institute of Health (NIH) consensus criteria Not suitable for, or declined high dose chemotherapy and autologous stem cell transplantation (ASCT). Prior autologous stem cell transplantation. Patients who have received prior stem cell transplantation will be allowed to enroll as long as prior transplantation has been at least 3 months before enrollment in the trial and any transplant related toxicities have subsided to grade 1 or less Patients must have failed at least 1 prior regimen before ibrutinib (not including single agent rituximab or single agent corticosteroids)\r\n* Note: any relapse after prior autologous stem cell transplantation (SCT) will make the patient eligible regardless of other prior therapy Patients who have undergone autologous stem cell transplantation within 3 months from study entry Tandem autologous transplantation DONOR SELECTION: Not applicable; this protocol employs autologous transplantation, utilizing the patient’s own hematopoietic stem cells obtained from either the peripheral blood or bone marrow Patients with B-lineage ALL at least marrow CR in Salvage 1 and beyond with molecular failure at any time point after 1 month of salvage therapy are allowed, including patients who received prior allogeneic stem cell transplantation Patients who have poor or no graft function post stem cell transplantation Patients must have undergone autologous stem cell transplantation, within 18 months of initiation of induction therapy for newly diagnosed myeloma Prior autologous hematopoietic progenitor cell transplantation if the conditioning regimen included total body irradiation Patients should have received single autologous stem cell transplantation 60-120 days prior to enrollment to the trial DIAGNOSIS REQUIREMENT FOR PHASE I PATIENTS: High-risk AML (by European Leukemia Net [ELN] criteria) in complete remission (CR) and has either refused hematopoietic stem cell transplantation OR is currently not eligible for hematopoietic stem cell transplantation OR for whom hematopoietic stem cell transplantation is being reserved for later relapse; this is inclusive of patients with minimal residual disease evidenced by cytogenetics, molecular testing, and/or flow cytometry OR Patients must be eligible to undergo autologous stem cell transplantation by standard institutional criteria Patients must have relapsed after high-dose therapy and autologous transplantation or be ineligible for high-dose therapy and autologous transplantation; patients that have failed autologous transplantation are those with persistent disease > 30 days after transplant; those ineligible for autologous transplant include those with chemoresistant disease (i.e., patients who have not achieved a partial response or better with their most recent chemotherapy regimen), are expected to have a poor outcome from autologous transplant (e.g., DLBCL relapsing within one year of rituximab, cyclophosphamide, doxorubicin hydrochloride, vincristine sulfate, prednisone [R-CHOP]-like chemotherapy, double hit lymphoma, v-myc myelocytomatosis viral oncogene homolog (avian) positive [MYC+] lymphoma, persistent positron emission tomography [PET] positivity after chemotherapy), are unable to collect sufficient or tumor-free autologous stem cells per Seattle Cancer Care Alliance (SCCA) standard practice, are unable to tolerate the high-dose autologous conditioning regimens, or who refuse a high-dose autologous transplant regimen Multiple myeloma with disease in the following categories:\r\n* Patients with relapsed multiple myeloma following autologous stem cell transplantation who have achieved at least partial response following additional chemotherapy\r\n* Patients with high risk cytogenetics at diagnosis must have achieved at least a partial response following autologous stem cell transplantation; patients must have complex karyotype, del17p, t4;14 and/or t14;16 by fluorescent in situ hybridization (FISH) and/or del13 by karyotyping Multiple myeloma (MM) stage II or III patients who have progressed after an initial response to chemotherapy or autologous hematopoietic stem cell transplantation (HSCT) or MM patients with refractory disease who may benefit from tandem autologous-nonmyeloablative allogeneic transplant Patients with stored autologous stem cells will be allowed Minimum donor and stem cell requirements for high-risk patients undergoing stem cell transplantation: Patients must be ineligible for autologous transplantation due to prior autologous transplant, an inadequate autologous stem cell harvest, inability to withstand a myeloablative preparative regimen, or clinically aggressive/high risk disease Stem cells: patients must have an autologous hematopoietic stem cell product cryopreserved and available for re-infusion after MIBG treatment; the minimum dose for peripheral blood stem cells is 2 x 10^6 CD34+ cells/kg Autologous stem cell transplantation less than 90 days prior to study day 1 Patients who have received prior stem cell transplantation will be allowed to enroll as long as prior transplantation has been at least 3 months before enrollment in the trial and any transplant related toxicities have subsided to grade 1 or less Have received or are ineligible for immediate established curative regimens, including stem cell transplantation Patients who have undergone autologous stem cell transplantation (ASCT) are eligible provided that they are >= 4 weeks from stem cell infusion and meet other eligibility criteria Eligible for autologous transplantation Prior high-dose chemotherapy and autologous hematopoietic cell transplantation (HCT)(s) is (are) allowed Considered by the investigator to be eligible for high-dose chemotherapy (HDT) and autologous stem cell transplantation (ASCT) according to the institution's criteria based on age, medical history, cardiac and pulmonary status, overall health and condition, co-morbid condition(s), physical examination, and laboratory studies Completion of, if applicable, an autologous stem cell transplantation (ASCT) at least 3 months prior to first dose of study drug. Not a candidate for curative therapy or hematopoietic stem-cell transplantation (either due to disease burden, fitness, or preference). Has received autologous stem cell transplantation (ASCT) within 12 weeks before the date of randomization. Participant must be ineligible or unwilling to undergo stem cell transplantation at time of study entry Patients who have undergone autologous hematopoietic stem cell transplantation are eligible once they have recovered from all toxicities from therapy Subject must have documented diagnosis with previously untreated (for cohort C, the induction and consolidation treatment along with the first Autologous stem cell transplantation (ASCT) are allowed), symptomatic Multiple Myeloma (MM) as defined by the criteria below: Autologous hematopoietic cell infusion after high dose therapy At least 60 days Patients must have undergone autologous hematopoietic stem cell transplantation (AHCT) and achieved engraftment by day (D)60-180 as evidenced by absolute neutrophil count (ANC) > 1000/mcL and platelets (Plt) > 75,000/mcL Eligible for autologous stem cell transplantation The subject must not be a candidate for potentially curative therapy including hematopoietic stem cell transplantation, except where one of the standard therapy regimen combinations may be used prior to transplantation per standard medical practice The disease needs to be in one of the following stages:\r\n* At diagnosis or in first relapse AND the patient is unable to receive conventional chemotherapy for his/her condition\r\n* In second or subsequent relapse\r\n* With residual disease after autologous, syngeneic or allogeneic hematopoietic stem cell transplantation (HSCT) Any previous autologous hematopoietic stem cell transplantation (HSCT) must have occurred at least 3 months prior to start of conditioning Diagnosed with AML and eligible for standard induction chemotherapy or stem cell transplantation For rituximab + Atezo + Pola treatment group: relapsed or refractory DLBCL after treatment with at least one prior chemoimmunotherapy regimen that included an anti-CD20 monoclonal antibody, in participants who are not eligible for second line combination (immuno-) chemotherapy and autologous stem-cell transplantation or who have failed second line combination (immuno-) chemotherapy or experienced disease progression following autologous stem-cell transplantation Eligible for autologous stem cell transplantation Has received high dose chemotherapy followed by autologous stem cell transplantation less than 90 days prior to first dose of study treatment Participants who are newly diagnosed and not considered candidate for high-dose chemotherapy with stem cell transplantation (SCT) due to: being age >=65 years, or in participants <65 years: presence of important comorbid conditions likely to have a negative impact on tolerability of high dose chemotherapy with stem cell transplantation Patients must have received at least two prior lines of therapy and also must be refractory to lenalidomide (defined as progression while on active therapy or within 60 days of discontinuation); one prior line of therapy may consist of all predetermined components of induction followed by autologous stem cell transplantation and maintenance Research participant has an indication to be considered for autologous stem cell transplantation Research participant did not have evidence of disease progression after salvage therapy and therefore underwent an autologous myeloablative transplantation with hematopoietic progenitor cell autologous (HPC[A]) rescue procedure Prior solid organ transplantation or allogenic stem cell transplantation (ASCT). However, previous autologous BM transplant (ABMT) or autologous peripheral blood stem cell transplant (PBSCT) is permitted. Patients for whom lenalidomide and dexamethasone treatment is appropriate and who are not eligible for high-dose therapy followed by stem-cell transplantation (HDT-SCT) for 1 or more of the following reasons: Patient is considered for autologous stem cell transplantation with full dose melphalan (200 mg/m^2) Patients with relapsed multiple myeloma following autologous stem cell transplantation who achieved < partial response following additional chemotherapy or who achieved < partial response (PR) at 3 months following autologous stem cell transplantation and patients with plasma cell leukemia at diagnosis Patient must have undergone autologous stem cell transplantation, with melphalan as a preparative regimen, within 12 months of initiation of induction therapy for newly diagnosed myeloma Patients who have previously received an autologous stem cell transplantation must be at least 4 weeks post-transplant before study drug administration and must have exhibited a full haematological recovery Patients who are eligible for autologous transplantation Patients with histologically confirmed CD20 positive B-cell non-Hodgkin lymphoma (NHL) who are candidates for autologous stem cell transplantation (SCT) Participants must have a diagnosis of multiple myeloma documented by having > 15% plasma cells on bone marrow biopsy and/or monoclonal protein in blood and/or urine; all patients must have disease which is either stable or responsive after a minimum of 2 cycles of conventional chemotherapy and slated to undergo autologous peripheral blood stem cell transplantation incorporating mobilization chemotherapy for peripheral blood stem cell collection Phase I: Patients with diagnosis of multiple myeloma at any stage of disease undergoing high dose chemotherapy and stem cell transplantation; Phase II: Patients with myeloma undergoing a first high dose chemotherapy and stem cell transplantation after achieving at least stable disease following induction therapy; any induction regimen prior to transplantation is allowed; no more than 2 prior lines of therapy prior to transplantation are allowed Patients with relapsed multiple myeloma following autologous stem cell transplantation must have achieved at least partial response following additional chemotherapy (cohort 1):\r\n* Patients are eligible if relapse occurs with complex/high-risk cytogenetics or occurs with normal cytogenetics but within 15 months following the autologous transplant Patients with high risk cytogenetics at diagnosis must have achieved at least very good partial response following autologous stem cell transplantation (cohort 2):\r\n* Patients must have complex karyotype, 1q25, del17p, t4;14 and/or t14;16 by fluorescence in situ hybridization (FISH) and/or del13 by karyotyping Patients achieving < partial response following preceding chemotherapy (cohort 1) or < very good partial response following autologous stem cell transplantation (cohort 2) Eligibility for potentially-curative therapy including hematopoietic stem-cell transplantation Progressive disease within 8 weeks of prior therapy or within 12 weeks after prior autologous stem cell transplantation Greater than approximately 6 months since autologous stem cell transplantation Subjects with AML in their first relapse following a remission >12 months in duration who are eligible for standard therapies (e.g. chemotherapy or stem cell transplantation); Patients with neutropenic fever who have existing malignancy or have undergone hematopoietic stem cell transplantation Patients who are candidates for autologous stem-cell transplantation due to primary refractory or first relapse of disease Patients with adequate autologous stem cell collection for transplantation (target >= 2.5 x 10^6 CD34+ cells/kg) Patients with newly diagnosed double hit in first complete remission, anytime during the first 3 months after chemoimmunotherapy followed by autologous stem cell transplantation if there was no evidence of progression Must have received at least 2 prior therapies, including a CD20 targeted therapy, alkylating agent or corticosteroid; subjects who are not eligible for high-dose chemotherapy and autologous stem cell transplantation (HD-ASCT) are eligible with exposure to at least 1 prior therapy. Waldstrom's Macroglobulinemia Dose Expansion Arm: “Relapsed or refractory” refers to patients who have received at least 1 prior treatment regimen for lymphoma (which may include prior autologous stem cell transplantation) and have demonstrated evidence of progressive disease by clinical and/or radiographic characteristics Eligible for autologous transplantation Previous autologous stem cell collection Eligible for autologous stem cell transplantation Prior therapy with severely myelotoxic regimens, including autologous and allogenic stem cell transplantation At least 1 prior specific therapeutic regimen, one of which should have included rituximab (patients previously eligible for transplantation: the salvage treatment followed by intensification and Autologous Stem Cell Transplant (ASCT) will be considered one regimen). Patients must have relapsed or progressed after at least one prior cytotoxic chemotherapy\r\n* Previous autologous or allogeneic stem cell transplantation is permitted\r\n* Previous treatment with either single agent panobinostat or lenalidomide is permitted Patients who are candidates for high dose chemotherapy and autologous stem cell transplantation with curative intent should not be enrolled Previous autologous stem cell transplantation within 6 months prior to randomization. The patient has received, or is receiving induction chemotherapy followed by Stem Cell Transplantation. The patient declines to undergo stem cell transplantation or Stem cell transplantation is not available to the patient due to cost or other reasons At the discretion of the principal investigator if he/she feels that the patient is unable to safely complete the study; specifically, patients must be considered medically eligible to undergo high dose chemotherapy and autologous stem cell transplantation Prior autologous stem cell transplantation < 1 month or allogenic stem cell transplantation < 3 months prior to C1D1. Prior allogeneic hematopoietic stem-cell transplantation if evidence of donor chimerism persists; patients with exclusively autologous hematopoiesis are eligible Patients who will undergo their first autologous hematopoietic stem cell transplantation (HSCT) procedure as treatment for multiple myeloma All patients must have a histologic or cytological diagnosis of ALL treated with stem cell transplantation; there are no restrictions on prior therapy Scheduled to receive conditioning chemotherapy followed by upfront or salvage autologous peripheral blood hematopoietic stem cell transplantation Patients with pathologically diagnosed who have received induction chemotherapy, with or without autologous stem cell transplantation (AuSCT), and who have qualified to receive lenalidomide-based maintenance therapy for their multiple myeloma (MM) Allogeneic stem cell transplantation using in vivo or ex vivo T cell depletion, either by cell manipulation or with T cell depleting antibodies (any anti-thymocyte globulin preparation or alemtuzumab given within 30 days of transplantation) Subjects with hematologic malignancies or recipients of a first allogeneic or autologous hematopoietic stem cell transplantation and presently clinically stable Eligible for haploidentical stem cell transplantation according to the investigator Autologous stem cell transplantation less than 90 days prior to study day 1 Patients receiving autologous stem cell transplantation must wait 8 weeks before initiation of study drug administration. Not a candidate for or refusing treatment with hematopoietic stem cell transplantation Not a candidate for, or refusing treatment with hematopoietic stem cell transplantation Patients must have received 4 or more cycles of one of the following prior systemic induction chemotherapy regimens:\r\n* Rituximab, cyclophosphamide, doxorubicin hydrochloride (hydroxydaunomycin), vincristine sulfate (Oncovin), prednisone (R-CHOP) (with or without cytarabine-containing cycles, including “Nordic” and European Mantle Cell Lymphoma Network [MCL-NET] protocols) with or without autologous (auto) stem cell transplant (SCT)\r\n* R-Hyper-cyclophosphamide, vincristine sulfate, doxorubicin hydrochloride (adriamycin), dexamethasone (CVAD) with or without auto SCT\r\n* Bendamustine + rituximab with or without auto SCT\r\n** Please note:\r\n*** Patients are allowed to receive combinations of the above regimens\r\n*** At the time of registration, patients must be at least 14 days out from last dose of cytotoxic chemotherapy, but no more than 120 days; if a patient underwent auto SCT, he/she must demonstrate engraftment (per treating investigator's discretion) and meet all other hematological requirements as outlined below\r\n*** Patients who progress during induction therapy are not eligible to enroll in this study Patients who have had a prior allogeneic stem cell transplant are not eligible\r\n* NOTE: if a patient underwent auto SCT, he/she must demonstrate engraftment (per treating investigator’s discretion) and meet all other hematological requirements Autologous stem cell transplantation (SCT) within 100 days prior to first infusion Completion of autologous SCT within 100 days prior to Day 1 of Cycle 1 Prior allogeneic stem-cell transplantation (SCT), or autologous SCT within 100 days prior to Day 1 of Cycle 1 Stem Cell Transplant (SCT): No evidence of active graft versus host disease. For allogeneic SCT, greater than or equal to 6 months must have elapsed. Any patient, regardless of age or sex, with Epstein-Barr virus (EBV)-positive lymphoma, or lymphoepithelioma regardless of the histological subtype or EBV (associated)-T/natural killer (NK)-lymphoproliferative disorder (LPD) all confirmed on any tissue sample\r\n* Primary refractory lymphoma or in second or subsequent relapse including after autologous or syngeneic stem cell transplant OR patients at a high risk for relapse defined as: (i) patients with primary refractory lymphoma or multiply relapsed lymphoma who are in remission but not eligible for autologous stem cell transplant (SCT) or (ii) patients with relapsed lymphoma after autologous SCT who are in remission but not eligible for allogeneic SCT (Group A) OR\r\n* Any patient who has received an allogeneic SCT for EBV lymphoma or EBV (associated)-T/NK-LPD or lymphoepithelioma (Group B) In view of the principal investigator (PI) and the primary oncologist, there must be no available alternative curative therapies or subject has declined to pursue alternative therapy; and subjects must be either ineligible for allogeneic stem cell transplant (SCT), have refused SCT, recurred after SCT, or have disease activity that prohibits SCT at the time of enrollment\r\n* Chemotherapy refractory disease in subjects with B-ALL is defined as progression or stable disease after two lines of therapies\r\n* Recurrence of disease after achieving a complete response (CR)\r\n* Subjects with persistent or relapsed minimal residual disease (MRD) (by flow cytometry, polymerase chain reaction [PCR], fluorescence in situ hybridization [FISH], or next generation sequencing) require verification of MRD positivity on two occasions at least 4 weeks apart\r\n* Subjects with Philadelphia chromosome positive acute lymphoblastic leukemia (Ph+ALL) subjects are eligible if they progressed, had stable disease or relapsed after two lines of therapy, including tyrosine kinase inhibitors (TKIs)\r\n* Subjects with recurrence of isolated central nervous system (CNS) relapse after achieving complete remission (CR); if relapsed with MRD, will require verification of MRD positivity on two occasions at least 4 weeks apart Subjects who have undergone autologous SCT with disease progression or relapse following SCT will be eligible if all other eligibility criteria are met; subjects who have undergone allogeneic SCT will be eligible if, in addition to meeting other eligibility criteria, they are at least 100 days post-transplant, they have no evidence of active graft versus host disease (GVHD) and have been without immunosuppressive agents for at least 30 days Who have received autologous stem cell transplant (SCT) 60 days before first infusion of TAK-573 or participants who have received allogeneic SCT 6 months before first infusion. Graft-versus-host disease that is active or requires ongoing systemic immunosuppression. Prior allogeneic stem cell transplantation (SCT), or autologous SCT within 100 days prior to Day 1 of Cycle 1 Patient must have a B cell acute lymphoblastic leukemia (ALL) (inclusive of ALL blast transformation from chronic myelogenous leukemia [CML]) or lymphoma and must have relapsed or refractory disease after at least one standard chemotherapy regimen and one salvage regimen; in view of the principal investigator (PI) and the primary oncologist, there must be no available alternative curative therapies and subjects must be either ineligible for allogeneic stem cell transplant (SCT), have refused SCT, recurred after SCT, or have disease activity that prohibits SCT at the time of enrollment Prior stem-cell transplantation (SCT). Must have undergone an allogeneic SCT (regardless of stem cell source) Prior autologous or allogeneic stem cell transplant (SCT) Administration of chemotherapy, biological, immunotherapy, or investigational agent (therapeutic or diagnostic) within 3 weeks before enrollment (14 days for non-myelosuppressive therapy). Subjects should be 6 weeks from last dose of nitrosourea, nitrogen mustards or monoclonal antibody, 12 weeks from autologous stem cell transplantation (SCT), and 16 weeks from allogeneic SCT Patient must have a B cell ALL (inclusive of chronic myeloid leukemia [CML] with ALL transformation) or lymphoma and must have relapsed or refractory disease after at least one standard chemotherapy regimen and one salvage regimen; in view of the principal investigator (PI) and the primary oncologist, there must be no available alternative curative therapies and subjects must be either ineligible for allogeneic stem cell transplant (SCT), have refused SCT, recurred after SCT, or have disease activity that prohibits SCT at the time of enrollment; patients who have undergone autologous SCT will be eligible, and patients that have undergone allogeneic SCT will be eligible if, in addition to meeting other eligibility criteria, they have no evidence of graft versus host disease (GVHD) and have been without immunosuppressive agents for at least 30 days; patients with Philadelphia chromosome + ALL must have failed prior tyrosine kinase inhibitor; patients must have measurable or evaluable disease at the time of enrollment, which may include any evidence of disease including minimal residual disease detected by flow cytometry Relapse after SCT is allowed but no active graft-versus-host disease (GVHD) as per treating physician; also must not exceed the number of prior induction regimens listed above; SCT does not count as line of therapy Relapsed and/or refractory disease as defined by: a. Clonal relapse after at least one previous line of therapy or high-dose chemotherapy and autologous stem cell transplantation OR b. Refractory disease to prior therapy defined as less than a hematologic very good partial response (VGPR). If previous therapy was autologous stem cell transplant (SCT), must be >= 3 months after SCT Subjects who have undergone autologous stem cell transplantation (SCT) with disease progression or relapse following SCT are eligible; subjects who have undergone allogeneic SCT will be eligible if, in addition to meeting other eligibility criteria, they are at least 100 days post transplant, they have no evidence of graft versus host disease (GVHD) and have been without immunosuppressive agents for at least 30 days Be able to start the drug therapy between 42 to 100 days following allogeneic SCT;\r\n* No more than 1 prior allogeneic SCT\r\n* Post-transplant bone marrow consistent with complete remission with no evidence of minimal residual disease by flow-cytometry or cytogenetics or molecular testing\r\n* Adequate engraftment within 14 days prior to starting study drug: absolute neutrophil count (ANC) >= 1.0 x 10^9/L without daily use of myeloid growth factor; and, platelet >= 50 x 10^9/L without platelet transfusion within 1 week No further chemotherapy or stem cell transplant (SCT) planned at the time of enrollment Patients must be eligible for one of two cohorts: cohort 1 (FLT3 and/or FLT3-D835 inhibitor failure cohort) in FLT3-ITD and/or FLT3-D835 mutated relapsed/refractory AML who have failed therapy with up to two prior salvage regimens (stem cell transplant [SCT] or stem cell therapy for patients who previously underwent SCT/stem cell therapy in remission will not be considered a salvage regimen) and have previously been exposed at least one prior FLT3 inhibitor; cohort 2 (FLT3 inhibitor naive cohort) in FLT3-ITD and/or FLT3-D835 mutated relapsed/refractory who have failed therapy with up to two prior salvage regimens (SCT or stem cell therapy for patients who previously underwent SCT/stem cell therapy in remission will not be considered a salvage regimen) with no prior exposure to any FLT3 inhibitor Prior autologous stem cell transplant (SCT) in the prior 12 months Stem cell transplant (SCT): at least 8 weeks following autologous SCT and 12 weeks for allogeneic SCT TREATMENT: Diagnosis of myeloma after receiving at least one treatment regimen; if patient has received an autologous or syngeneic stem cell transplant (SCT) they must be > 90 days post-transplant (Group A) OR\r\nfollowing autologous or syngeneic SCT (as adjuvant therapy) and < 90 days post-transplant (Group B) Patients should have received the autologous SCT within 12 months of their diagnosis of myeloma to be eligible for the study Prior allogeneic SCT Prior autologous SCT in last 12 months Subjects with CD19+ B cell lymphomas with no available curative treatment options (such as autologous or allogeneic stem cell transplant [SCT]) who have a limited prognosis (several months to < 2 year survival) with currently available therapies Mantle cell lymphoma\r\n* Beyond 1st CR with relapsed disease, progressive disease during first line rituximab-chemotherapy combination, or persistent disease after first line rituximab-chemotherapy combination and not eligible or appropriate for conventional allogeneic or autologous SCT\r\n* Relapsed after prior autologous SCT Diffuse large B cell lymphoma, previously identified as CD19+\r\n* Residual disease after primary therapy and not eligible for autologous SCT\r\n* Relapsed or persistent disease after prior autologous SCT\r\n* Beyond 1st CR with relapsed or persistent disease and not eligible or appropriate for conventional allogeneic or autologous SCT\r\n* Patients with an antecedent history of follicular lymphoma or chronic lymphocytic leukemia (CLL)/small lymphocytic lymphoma (SLL) are eligible Any relapse after prior autologous SCT will make patient eligible regardless of other prior therapy Prior autologous stem-cell transplant (SCT) in the prior 3 months Prior allogeneic hematopoietic SCT within the last 12 months or reduced-intensity transplant within the past 6 months Patients with lymphomas: prior allogeneic SCT Patient requiring allogeneic SCT Allogeneic SCT recipient requiring additional cellular therapy Prior autologous or allogeneic hematopoietic cell transplantation (other than autologous SCT 60-120 days prior to registration) Known or suspected progressive disease following autologous SCT Additional treatment for NHL administered from time of autologous SCT through registration Are planning to undergo SCT prior to PD on this study (ie, these participants should not be enrolled in order to reduce disease burden prior to transplant). Has received autologous SCT within 12 weeks before the date of study treatment. Subjects with a history of autologous SCT, are eligible for study participation provided the following eligibility criteria are met: Autologous SCT was >100 days prior to study enrollment; No active bacterial, viral, or fungal infection(s) present; Subject meets the remainder of the eligibility criteria. Prior treatment with any of the following: allogeneic or syngeneic SCT within 16 weeks prior to randomization; or autologous SCT within 12 weeks prior to randomization. Stem cell transplant (SCT): no evidence of active graft vs. host disease for at least 4 weeks; for allogeneic SCT patients, >= 3 months must have elapsed since transplant\r\n* Must have received no more than 1 prior autologous or allogeneic stem cell transplant.\r\n* Patients must be off all systemic immunosuppressive therapy for at least 2 weeks, excluding hydrocortisone for physiologic cortisol replacement Patient must have a CD19-expressing B cell acute lymphoblastic leukemia (ALL) or lymphoma and must have relapsed or refractory disease after at least one standard chemotherapy and one salvage regimen; in view of the principal investigator (PI) and the primary oncologist, there must be no available alternative curative therapies and subjects must be either ineligible for allogeneic stem cell transplant (SCT), have refused SCT, or have disease activity that prohibits SCT at this time Multiple myeloma\r\n* Primary treatment failure\r\n* Relapse after autologous SCT or for consolidation after autologous SCT\r\n* Non-CR after salvage regimen Ineligible to receive treatment with auto-SCT due to age (?65 years old) or any significant coexisting medical condition (cardiac, renal, pulmonary or hepatic dysfunction), likely to have a negative impact on tolerability of auto-SCT. Participants <65 years of age who refuse auto-SCT are not eligible for this study. Has relapsed after autologous stem cell transplant (auto-SCT) or has failed to achieve a Complete Response or Partial Response within 60 days of auto-SCT. Participants may have received intervening therapy after auto-SCT for relapsed or refractory disease, in which case they must have relapsed after or be refractory to their last treatment. OR Any BM relapse after allogeneic SCT and must be > 6 months from SCT at the time of CTL019 infusion OR Ineligible for allogeneic SCT Has received autologous stem cell transplant (auto-SCT) within 12 weeks before the first infusion or is planning for or is eligible for auto-SCT Have had at least 60 days between prior hematopoietic stem cell transplantation (SCT) and first dose of study drug. Any BM relapse after allogeneic stem cell transplantation (SCT) and must be ? 6 months from SCT at the time of CTL019 infusion OR. Ineligible for allogeneic SCT. Completion of autologous stem cell transplant (SCT) within 100 days prior study start Prior allogeneic SCT Eligibility for autologous SCT (participants with r/r DLBCL) Completion of autologous SCT within 100 days prior to Day (D) 1 of Cycle (C) 1 Autologous stem cell transplantation (SCT) within 100 days prior to study drug, or any prior allogeneic SCT or solid organ transplantation Prior allogeneic stem cell transplantation (SCT), completion of autologous SCT within 100 days prior to Day 1 of Cycle 1 (D1C1) Participant may have failed to achieve a response to, progressed after, or be ineligible for autologous stem cell transplant (auto-SCT) Prior allogeneic stem cell transplant (SCT) within 16 weeks or autologous SCT within 8 weeks of initiation of therapy (patients that require immunosuppressive therapy are not eligible within 60 days of therapy) Subject is a candidate for high-dose therapy and autologous SCT based on standard criteria at the institution where this treatment will be administered Prior allogeneic stem cell transplant (SCT) within 16 weeks or autologous SCT within 8 weeks of initiation of therapy; (patients that require immunosuppressive therapy are not eligible within 60 days of therapy) Autologous SCT within 8 weeks and allogeneic SCT within 16 weeks prior to initiation of study treatment. Patients with prior allogeneic SCT should not have evidence of moderate-to-severe graft-versus-host disease (as defined in Filipovich 2005). May include prior auto-SCT but not prior allo-SCT Patients who have failed second or third line therapy and beyond, such as DPACE, and who are experiencing a partial response rather than progressive disease are also eligible. Immunotherapy/standard myeloma therapy within 2 weeks; prior stem cell transplant (SCT) therapy (autologous SCT within the prior 8 weeks; allogeneic SCT within the prior 16 weeks) Any relapse after prior autologous SCT will make patient eligible regardless of other prior therapy Patient must be determined fit to undergo auto-SCT procedure by a study physician Autologous SCT within 12 weeks prior to study entry (Arms A and D only) Prior allogeneic SCT or organ transplant (Arms A and D only) Prior allogeneic stem cell transplantation (SCT), or autologous SCT within 100 days prior to Day 1 of Cycle 1 Prior autologous or allogeneic stem cell transplant (SCT)/bone marrow transplant within 12 months of signing the ICD. Subjects who received allogeneic SCT ? 12 months before signing the ICD may be eligible provided there is no ongoing graft-versus-host disease and no ongoing immune suppression therapy. frontline cytotoxic systemic therapy, for patients who are ineligible for stem cell transplant (SCT). Completion of autologous stem cell transplant (SCT) within 100 days prior to Cycle 1 Day 1 Prior allogeneic SCT Eligibility for autologous SCT Prior autologous or allogeneic SCT Is indicated with standard melphalan prednisone (MP) treatment and is not a candidate for high-dose therapy plus stem cell transplantation (HDT-SCT) for 1 of the following reasons: the participant is 65 years of age or older OR the participant is less than 65 years of age but has significant comorbid condition(s) that are likely to have a negative impact on tolerability of HDT-SCT PRE-STEM CELL TRANSPLANT (SCT) PRE-SCT Prior allogeneic SCT Be planning to receive a conditioning regimen for stem cell transplant (SCT) consisting of cyclophosphamide and total body irradiation and must meet inclusion criteria for SCT which include: Patients with a prior stem cell transplant (SCT) must have failed the SCT Non-allogeneic (e.g. autologous) or syngeneic hematopoietic stem cell transplant (SCT) recipients Non-allogeneic (e.g. autologous) or syngeneic hematopoietic stem cell transplant (SCT) recipients Patients who have previously undergone hematopoietic stem cell transplantation (SCT) or who are scheduled for SCT Prior autologous or allogeneic stem cell transplantation (SCT) within 12 weeks of initiation of study treatment Disease progression or recurrence less than or equal to 12 months of prior autologous SCT History of allogeneic organ transplantation CRITERIA FOR ALLOGENEIC TRANSPLANTATION Prior autologous or allogeneic organ or tissue transplantation History of allogeneic organ transplantation. Patients who are candidates for allogeneic transplantation, have a suitable donor, and are willing to undergo transplantation Anticipated liver transplantation Prior allogeneic transplantation Previous allogeneic or autologous hematopoietic cell transplantation or solid organ transplantation Patients with prior orthotropic liver transplantation History of allogeneic organ transplantation Allogeneic hematopoietic cell transplantation within 5 years of study drug administration Patients who have undergone prior liver transplantation are ineligible PHASE I: Patients who are between T+40 and T+100 after allogeneic transplantation PHASE I: Patients who have evidence of donor chimerism after allogeneic transplantation PHASE II: Patients who are between T+40 and T+100 after allogeneic transplantation PHASE II: Patients who have >= 80% donor chimerism after allogeneic transplantation ADDITIONAL INCLUSION CRITERIA PERTINENT ONLY FOR PATIENTS WITH PRIOR ALLOGENEIC TRANSPLANTATION: Prior hematopoietic transplantation is allowed (autologous and/or allogeneic) Patients with any of the following hematologic malignancies who are considered to be eligible for allogeneic transplantation: Prior history of allogeneic hematopoietic cell transplantation Patients who have undergone prior liver transplantation are ineligible Relapsed after allogeneic transplantation Prior hematopoietic transplantation is allowed (autologous and/or allogeneic) Use of any of the following after transplantation and prior to starting study therapy: Prior high dose chemotherapy for autologous hematopoietic cell transplantation or prior allogeneic transplantation Relapsed malignancy after transplantation Prior allogeneic or autologous transplantation Prior allogeneic hematopoietic progenitor cell transplantation Transplantation for AML (allogeneic or autologous) allowed unless within 90 days of study entry Relapsed after allogeneic transplantation Patients with B-cell hematological malignancies who are eligible for allogeneic transplantation At least 60 days from day of transplantation Prior autologous or allogeneic organ or tissue transplantation Patients considered for transplantation must have a sufficient graft as based on current criteria of the University of Minnesota Blood and Marrow Transplantation Program Time available (at least 12 weeks) for treatment of hepatitis C prior to autologous or allogeneic transplantation History of allogeneic organ transplantation History of allogeneic organ transplantation. Prior autologous or allogeneic organ or tissue transplantation Prior autologous or allogeneic transplantation for any disease No prior autologous or allogeneic organ or tissue transplantation History of allogeneic organ transplantation. Prior hematopoietic cell transplantation allogeneic or autologous (A prior autologous HCT will be allowed as long as it was part of tandem transplantation). Prior allogeneic hematopoietic cell transplantation ALLOGENEIC TRANSPLANTATION: Subjects who are candidates for allogeneic transplantation, have a suitable donor, and are willing to undergo transplantation Previous liver transplantation Prior allogeneic transplantation Patients who have undergone liver transplantation are excluded Prior allogeneic transplantation Patients must be between 2-6 months post-transplantation at the time of study registration Patients who have received liver transplantation History of allogeneic organ transplantation; History of allogeneic organ transplantation Subjects who relapse after allogeneic transplantation; Patients who have undergone prior liver transplantation are ineligible Prior liver transplantation and on immunosuppression Patients that underwent allogeneic transplantation as a treatment of graft failure Hepatitis A, B and C status will be tested prior to therapy, but results will not exclude patients from participation (if positive, patients will be told they are at higher risk of adverse effects from allogeneic transplantation) No prior autologous or allogeneic hematopoietic cell transplantation Patients that underwent allogeneic transplantation as a treatment of graft failure Patient must meet eligibility criteria for allogeneic transplantation Prior allograft transplantation including liver transplantation. Immunocompromised, as defined by one of the following: Autologous or Allogeneic hematopoietic cell transplantation (HSCT); Lung or lung-heart transplantation; Subjects treated with chemotherapy for hematologic malignancies; Subjects treated with chemotherapy for solid tumor malignancies Has received a prior allogeneic organ or tissue transplantation The participant has received a prior autologous or allogeneic organ or tissue transplantation. Patients who have undergone prior allogeneic transplantation are eligible provided that their transplant day 0 is > 6 months from their first dose of study drug Transplantation of PBSC Patients must have undergone an autologous transplant =< 12 months prior to allogeneic transplantation or have received multi-agent or immunosuppressive chemotherapy within 3 months of the preparative regimen Prior allogeneic transplantation Patients must have a hematologic malignancy for which allogeneic hematopoietic peripheral blood cell transplantation is deemed clinically appropriate. Eligible diseases and stages include the following: Prior allogeneic hematopoietic cell transplantation (HCT) Hematologic disorder requiring allogeneic hematopoietic cell transplantation Transplantation with PBSC Prior allogeneic transplantation Patients must not be candidates for allogeneic hematopoietic stem cell transplant; NOTE: Subjects up to age 70 years who are considered fit for allogeneic hematopoietic stem cell transplant, should be considered for enrollment on E1910, in order to avoid competing with that study; if a patient is considered unfit for intensive chemotherapy at the time of initial diagnosis, but subsequently achieves a complete remission (CR), then it will be left to the treating physician’s discretion to consider hematopoietic stem cell transplant (HSCT) ELIGIBILITY CRITERIA - PHASE II (ARM D): Patient may be enrolled with a prior allogeneic hematopoietic stem cell transplant (HSCT) but the transplant date must be at least 90 days before date of enrollment; patient must be off immunosuppression and without active GVHD prior to enrollment if previous HSCT Gene therapy using an integrating vector Allogeneic hematopoietic stem cell transplant at any time not permitted Prior allogeneic hematopoietic cell transplant Subjects with prior autologous and allogeneic hematopoietic stem cell transplantation (allo HSCT) are eligible. Intention to proceed to high dose chemotherapy (HDT) and autologous hematopoietic stem cell transplant (HSCT) Adult male and female subjects at least 18 years of age who have had allogenic bone marrow transplant (BMT) or hematopoietic stem cell transplantation (HSCT). Prior allogeneic hematopoietic stem cell transplantation (allo HSCT) Prior allogeneic hematopoietic cell transplant Previous allogeneic hematopoietic stem cell transplant Allogeneic hematopoietic stem cell transplant Prior allogeneic transplant for any hematopoietic disorder Subject is a candidate for hematopoietic stem cell transplantation (HSCT). Prior cell or gene therapy, excluding transfers of genetically unmodified autologous cells (eg. Hematopoietic stem cell transplantation), at any time; or prior allogeneic HSCT at any time DONOR: Testing for communicable disease will be performed according to the University of Washington (UW) Hematopoietic Stem Cell Transplant Program guidelines set forth in the most current standard operating policies and procedures (UW Foundation for the Accreditation of Cellular Therapy [FACT]-accredited Clinical Hematopoietic Cell Processing Laboratory [CHCPL] standard of procedure [SOP]) for hematopoietic cell donor evaluation and selection Immunosuppression following a Hematopoietic Stem Cell Transplantation (HSCT) within 6 weeks prior to study entry; Allogeneic hematopoietic stem cell transplantation (HSCT) within 24 weeks before the start of protocol-specified therapy. Either not eligible or unwilling to proceed with hematopoietic stem cell transplantation (HSCT) Eligible for, have a suitable donor, and are willing to undergo hematopoietic stem cell transplantation (HSCT) Previous allogeneic hematopoietic cell transplant (HCT) History of hematopoietic stem cell transplant (HSCT) Has previously received an allogeneic hematopoietic cell transplant or chimeric antigen receptor-modified (CAR)-T cells Diagnosis of AML and MDS according to World Health Organization (WHO) classification that underwent first allogeneic hematopoietic cell transplant (HSCT) with either peripheral blood or bone marrow as the source of the hematopoietic stem cells Prior allogeneic hematopoietic cell transplant. Has received allogeneic hematopoietic stem cell transplant within 3 months of CAR T cell infusion; hematopoietic stem cell transplant (HSCT) > 3 months from CAR T cell infusion eligible Individuals who are eligible for allogeneic hematopoietic stem cell transplantation (HSCT) as determined by the treating physician, and have a suitable donor or appropriate stem cell source available Study enrollment no earlier than 3 months after preceding hematopoietic cell transplantation (HSCT) Patients who have received a prior allogeneic hematopoietic stem cell transplant (HSCT) and who have either rejected their grafts or who have become tolerant of their grafts with no active GVHD requiring immunosuppressive therapy Prior autologous or allogeneic hematopoietic stem cell Preceding allogeneic hematopoietic stem cell transplant (HSCT) - Participant is not a candidate to undergo intensive chemotherapy or allogeneic hematopoietic stem cell transplantation (HSCT). Malignant conditions or other life threatening disorders correctable by transplant for which CD34+ selected, T-cell depleted allogeneic hematopoietic stem cell transplantation is indicated such as: No subjects who have received an allogeneic hematopoietic stem cell transplant are eligible Received an allogeneic hematopoietic transplant within 3 months of screening Have active malignancy with the exception of nonmelanoma skin cancer. Subjects who have had a hematopoietic stem cell transplant (HSCT) and who experience relapse or progression of the malignancy as per investigator's opinion are not to be enrolled. Evidence of multiple myeloma disease progression (as defined by IMWG) any time prior to autologous (auto)-hematopoietic stem cell transplant (HSCT) Prior autologous or allogeneic hematopoietic stem cell transplantation (HSCT) Prior allogeneic transplant for any hematopoietic disorder Subject is refractory to or relapsed after first-line AML therapy (with or without hematopoietic stem cell transplant (HSCT)). Hematopoietic cell transplantation (At least 60 days from infusion of hematopoietic cells prior to first dose of tazemetostat) Prior allogeneic hematopoietic stem cell transplant. Subject who has history of organ transplant or allogeneic hematopoietic stem cell transplantation. Subjects with relapsed primary disease, or subjects who have been treated for relapse after the allogeneic hematopoietic stem-cell transplantation (allo-HSCT) was performed. Prior allogeneic hematopoietic stem cell transplant (HSCT) with either standard or reduced intensity conditioning ? 6 months. Patients who have previously undergone allogeneic hematopoietic stem cell transplant will be excluded from this study The patient has received any hematopoietic stem cell transplantation (HSCT) ? 3 months prior to start of Investigational Product. Allogeneic hematopoietic stem cell transplant within 100 days prior to leukapheresis Prior history of allogeneic hematopoietic stem cell transplant (HSCT). Recipients of prior allogeneic hematopoietic stem cell transplant (HSCT) with active acute or chronic GVHD Prior allogeneic hematopoietic stem cell transplant Prior allogeneic hematopoietic stem cell transplant Hematopoietic stem cell transplant (HSCT) patients with symptomatic hemorrhagic cystitis (minimal grade 1 symptoms of HC per NCI criteria) and positive BKV in urine > 1 x 10^3 deoxyribonucleic acid (DNA) copies/ml Recipient of an hematopoietic stem cell transplantation (HSCT) Prior autologous or allogeneic hematopoietic stem cell transplant (HSCT) Prior allogeneic hematopoietic stem cell transplant. Prior allogeneic hematopoietic stem cell transplant (HSCT) Prior allogeneic hematopoietic stem cell transplant Patient must not be a candidate for an allo-hematopoietic stem cell transplant (HSCT) At least 100 days after receiving any allogeneic hematopoietic stem cell transplant AND Previous allogeneic hematopoietic stem cell transplant (HSCT transplant). Allogeneic hematopoietic stem cell transplant or Donor Lymphocyte Infusion within 90 days prior to to the first dose of study drug Prior allogeneic hematopoietic stem cell transplant Prior allogeneic hematopoietic stem cell transplant within = 0.01% disease by Seattle Children’s Hospital (SCH) or University of Washington (UW) Pathology Department following allogeneic HCT Patients with a nonmalignant disease treatable by allogeneic HCT AUTOLOGOUS APHERESIS: Patients with a history of prior allogeneic hematopoietic cell transplantation (HCT) must be clinically recovered from prior HCT therapy, have no evidence of active graft versus host disease (GVHD) and have not received a donor lymphocyte infusion (DLI) within the 28 days prior to apheresis MANUFACTURING SJCAR19: CD19+ ALL with any of the following:\r\n* Primary refractory disease despite at least 2 cycles of an intensive chemotherapy regimen designed to induce remission\r\n* Refractory disease despite salvage therapy\r\n* 2nd or greater relapse\r\n* Any relapse after allogeneic hematopoietic cell transplantation \r\n* 1st relapse if patient requires an allogeneic HCT as part of standard of care relapse therapy, but is found to be ineligible and/or unsuitable for HCT Patients with a prior autologous or allogeneic HCT Have received a T cell-depleted allogeneic (i.e., non-autologous) HCT within the previous 100 days. If post allogeneic HCT: Confirmed CD19+CD22+ leukemia recurrence defined as >= 0.01% disease following allogeneic HCT If relapse/refractory status with no prior history of allogeneic HCT (one of the following)\r\n* 2nd or greater marrow relapse, with or without extramedullary disease\r\n* 1st marrow relapse at end of 1st month of re-induction with marrow having >= 0.01% blast by morphology and/or MPF\r\n* Primary refractory as defined as having > 5% blasts by multi-parameter flow or polymerase chain reaction (PCR) after 2 or more separate induction regimens\r\n* Subject has indication for HCT but has been deemed ineligible, inclusive of persistent MRD prior to HCT Patients who have relapsed or have MRD after HCT may receive other agents for treatment of disease and remain eligible for the protocol Previous HCT Has had relapse prior to primary neutrophil engraftment or =< 21 days post HCT Ages =< 50 years with hematologic diseases treatable by allogeneic HCT who refuse a high-dose HCT; transplants must be approved for these inclusion criteria by the principal investigators at the collaborating centers and at FHCRC Aggressive nonHodgkin lymphomas (NHL) and other histologies such as diffuse large B cell NHL– not eligible for autologous HCT, not eligible for high-dose allogeneic HCT, or after failed autologous HCT If post allogeneic HCT: confirmed CD22+ leukemia recurrence defined as >= 0.01% disease by following allogeneic HCT If relapse/refractory status with no prior history of allogeneic HCT (one of the following)\r\n* 2nd or greater marrow relapse, with or without extramedullary disease\r\n* 1st marrow relapse at end of 1st month of re-induction with marrow having >= 0.01% blast by morphology and/or MPF\r\n* Primary refractory as defined as having > 5% blasts by multi-parameter flow after 2 or more separate induction regimens\r\n* Subject has indication for HCT but has been deemed ineligible, inclusive of persistent MRD Received an allogeneic HCT within the last 100 days; enrollment within 30-100 days after transplant, and after adequate recovery of counts Prior autologous or allogeneic HCT Prior allogeneic HCT RESEARCH SAMPLE COLLECTION: Myeloma patients who are not candidates for high-dose melphalan followed by autologous HCT based on institutional standards Received high-dose melphalan (>= 140 mg/m^2) followed by autologous HCT based on the institutional guidelines and within +45 and +180 after autologous HCT at the time of panobinostat maintenance initiation Patients must have achieved at least partial response (PR) prior to autologous HCT and must not have progressive disease (PD) prior to the initiation of maintenance therapy Prior allogeneic HCT Prior allogeneic HCT Subjects with second or subsequent relapse, any relapse refractory to salvage, or with persistent disease after at least two lines of therapy\r\n* Subjects with relapsed disease after prior allogeneic HCT (myeloablative or non-myeloablative) will be eligible if they meet all other inclusion criteria and\r\n** Have experienced graft rejection (no evidence of donor cells by short tandem repeat [STR] analysis on 2 occasions separated by at least 1 month), OR\r\n** Donor cells are present but there is no active graft-versus-host disease (GVHD), subject does not require immunosuppression and is more than 6 months from transplant\r\n** Have relapsed after prior syngeneic HCT and is more than 3 months from transplant\r\n* Subjects with relapsed disease after prior autologous HCT will be eligible if they meet all other inclusion criteria and it has been more than 3 months from transplant HCT-CI/age score =< 5 points (patients with greater than 5 points will be allowed for trial with approval of the PI and the co-PI or his designee; this is an adjustment to account for healthy patients who meet the spirit of this protocol but have histories that result in higher than HCT-CI 5 points HCT-CI/age score > 5 points (patients with greater than 5 points will be allowed for trial with approval of the principal investigator and the co-principal investigator or his designee; this is an adjustment to account for healthy patients who meet the spirit of this protocol but have histories that result in higher than HCT-CI 5 points Expected to undergo HCT within 120 days of enrollment Patients with:\r\n* CLL who are beyond first remission and who have failed combination chemoimmunotherapy with regimens containing a purine analogue and anti-CD20 antibody or who were not eligible for such therapy; patients with CLL for whom ibrutinib is now standard first line therapy, must have progressed on ibrutinib; patients with fludarabine refractory disease are eligible; patients may be treated following allogeneic hematopoietic cell transplant (HCT); for the concurrent ibrutinib cohort, patients must agree to continue on or be restarted on ibrutinib and must not have had prior intolerance to ibrutinib that would prevent this; patients managed with prior dose reductions for toxicity will continue at the reduced dose for the remainder of this study\r\n* Indolent NHL or mantle cell NHL who are beyond first remission and previously treated with chemoimmunotherapy or who were not eligible for such therapy; patients who have relapsed following autologous or allogeneic HCT are eligible\r\n* Aggressive NHL such as diffuse large B-cell lymphoma (DLBCL), who have relapsed or have residual disease following treatment with curative intent; patients should have relapsed following, or not be eligible for high-dose therapy and autologous HCT; patients with chemotherapy refractory disease or marrow involvement or comorbidities precluding successful autologous HCT are eligible; patients may be treated following allogeneic HCT\r\n* Patients with CD19 expressing, relapsed or refractory ALL\r\n* Patients with one of the above diagnoses whose disease state does not qualify but who have prognostic indicators that suggest a high risk of progression of disease may be screened and undergo leukapheresis; enrollment for T cell therapy would require meeting the full disease state eligibility Does not have any other active malignancy other than the one for which this HCT is indicated No prior allogeneic HCT, and no autologous HCT within the previous 12 months Patients who are currently undergoing or who previously underwent matched allogeneic HCT for:\r\n* AML: Prospective enrollment will now be limited to patients with relapsed disease (overt relapse or minimal residual disease) at any time post allogeneic HCT\r\n* MDS will no longer be a criterion for eligibility\r\n* CML will no longer be a criterion for eligibility Active bacterial infection within one week of HCT Active fungal infection at time of HCT First autologous or allogeneic HCT and hematologic disease in remission on initiation of antiviral therapy for hepatitis C infection If undergoing myeloablative allogeneic HCT: If undergoing non-myeloablative allogeneic HCT: Contraindication to haploidentical HCT as defined by the Investigator Ongoing systemic immunosuppressive therapy after haploidentical HCT Administration of G-CSF after haploidentical HCT CD3+ cells ? 100/µl at day of planned experimental infusion after haploidentical HCT Patients with prior allogeneic hematopoietic cell transplantation (HCT) must be at least 90 days post-HCT and must be on =< 20 mg of prednisone (or equivalent dose of an alternative corticosteroid) for treatment/prevention of graft-vs-host disease Patients with chemorefractory non-Hodgkin’s or Hodgkin’s lymphoma or multiple myeloma\r\n* Criteria for consideration of enrollment will include:\r\n** Primary refractory or refractory relapsed disease for which autologous hematopoietic cell transplantation (HCT) is unlikely to be beneficial\r\n** Relapse after autologous HCT\r\n** Ineligibility for standard myeloablative or nonmyeloablative allogeneic (allo)-HCT because of either lack of a donor or patient considerations\r\n*** Non-Hodgkin’s lymphoma, or Hodgkin’s lymphoma: primary refractory or refractory relapse\r\n*** Multiple myeloma; primary refractory or refractory relapse\r\n*** Patients with the above malignancies who have had a previous autologous or allogeneic bone marrow or stem cell transplant Patients with previous autologous or allogeneic HCT are allowed to enroll > 20% blast in the PB or BM prior to hematopoietic cell transplantation (HCT) or had leukemic transformation (> 20% blasts in PB or BM any time prior to HCT) Patient willing to consider HCT Prior allogeneic HCT Have previously received HCT Planning to receive autologous HCT per institutional standards as part of standard of care. Eligibility for autologous HCT should be based on institutional guidelines. However, at minimum all patients must meet the following criteria:\r\n* Karnofsky performance status (KPS) greater than 70\r\n* Cardiac left ventricular ejection fraction of greater than 40%\r\n* Calculated creatinine clearance of greater than 40 cc/min\r\n* Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) of less than 2 x upper limit of normal\r\n* Direct bilirubin of less than 2 x upper limit of normal Prior allogeneic HCT (prior autologous transplant is allowed regardless of response) Hematopoietic cell transplantation (HCT) recipients Relapse of primary hematologic malignancy that served as indication for HCT Prior allogeneic HCT. Ages =< 50 years of age with hematologic diseases treatable by allogeneic HCT who refuse a high-dose HCT; transplants must be approved for these inclusion criteria by the principal investigators at the collaborating centers and at FHCRC Recurrence or progression of primary malignancy after HCT Aggressive non-Hodgkin lymphomas (NHL) and other histologies such as diffuse large B cell (DLBC) NHL - a) not eligible for autologous HCT, b) not eligible for high-dose HCT, c) after failed autologous HCT, or d) be part of a tandem auto-allo approach for high risk patients Patients must be expected to have disease controlled for at least 60 days after HCT Patients eligible for a curative autologous HCT Patients who have received a prior allogeneic HCT must have no active GVHD requiring immunosuppressive therapy for at least 21 days prior to start of conditioning Patients will then be assigned to one of two cohorts:\r\n* Cohort 1 will include patients who have relapsed /progressed within the first 180 days post-transplant and who are still within 3 months from date of progression-relapse\r\n* Cohort 2 will include patients who have either i) relapsed/progressed beyond day 180 post-HCT, ii) those with persistent stable disease or persistent disease with regression between days 28-100 after allogeneic HCT, or iii) those who progressed or relapsed within 180 days after HCT but were not started on this protocol within 3 months from date of progression or relapse could also be enrolled under cohort 2\r\n** NOTE: the inclusion of patients with persistent stable or persistent regressing disease in this protocol is not meant to advocate treatment; however, if the attending physician is inclined to offer treatment then these patients would be eligible for this study Diagnosis of skin, gut and/or liver steroid-refractory GVHD by clinical assessment of treating physician following allogeneic HCT. Patients who fail to respond to steroids by 7 days are considered steroid-refractory No evidence of HCT graft failure or multi-organ failure Candidate committed to HCT independent of participation in this study, with the following requirements: Meets local transplant center eligibility requirements for HCT Prior allogeneic or autologous HCT or adoptive cellular therapies, including T-cell chimeric antigen receptor (CAR) therapy Diagnosis of a nonmalignant disorder considered treatable by HCT. Extramedullary disease noted during pre-HCT work up can receive a boost of radiation as clinically indicated Patient has any other active malignancy other than the one for which HCT is indicated Anti-thymocyte globulin, alemtuzumab, bortezomib, or cyclophosphamide administered within 14 days before or planned to receive with HCT conditioning or as part of GVHD prophylaxis in the 14 days after HCT Patients must be previously untreated with HCT Normal WBC (3.5-10.8 x 103µL), PLT (140-400 x 103µL), and HCT (37-52%) Prior to Administration of Ibrutinib (Day 60 to Day 90 post HCT) Planned use of post-HCT cyclophosphamide for GVHD prophylaxis T deplete HCT Adult caregivers of patients undergoing autologous or allogeneic HCT at Massachusetts General Hospital (MGH), and they must attend the HCT consent visit with the patient Received >= 1 autologous or allogeneic (related or unrelated) HCT with curative intent at a participating transplant center for a hematologic malignancy Survival 2-5 years after last HCT when first approached for enrollment Refusing to use contraception up to 90 days post-HCT At least 1 year after HCT Planned HCT with minimal to no-T cell depletion of graft Conditioning regimens 30 days (d) prior to trial participation and up to d28 post-HCT Patients considered by PIs/protocol team to have a complicated prior therapy or HCT regimen, or who have a low survival probability (e.g., refractory leukemia and/or undergoing 2nd HCT) Adult patients with hematologic malignancy who underwent an allogeneic HCT at least 3 months prior to study enrollment Patients with relapsed disease post-HCT Planned HCT with no ex-vivo T cell depletion of graft; conditioning and immunosuppressive regimens according to institutional guidelines are permitted Planned HCT with minimal to no-T cell depletion of graft Participants must be at least 100 days after HCT Adult (? 18 years at time of allogeneic HCT recipient at participating transplant centers) Survival 1-2 years after most recent HCT with no evidence of relapse, disease progression, or secondary cancer on last follow-up Patient may have received more than one HCT Participants must be at least 100 days after HCT Currently 2-10 years after first HCT Prior autologous or allogeneic HCT; RECIPIENT: Planned medications from the time of HCT to day 70 post?HCT Between day +60 and day +90 after allogeneic HCT Aggressive non-Hodgkin lymphomas (NHL) and other histologies such as diffuse large B-cell NHL – not eligible for autologous HCT, not eligible for high-dose allogeneic HCT, or after failed autologous HCT Patients must have either relapsed after previous high-dose chemotherapy and autologous or allogeneic HCT, or else be ineligible for such an approach due to age, failure to mobilize sufficient hematopoietic stem cells, medical comorbidities, or patient refusal Patients who refuse to be treated on a conventional autologous or allogeneic HCT protocol Patients eligible for and willing to receive potentially curative high-dose chemotherapy and autologous HCT Prior diagnosis of an acute leukemia or lymphoma or any receipt of HCT for a malignant condition. Planned haematopoietic stem cell transplant (HCT) during the study period. (If a HCT occurred prior to enrolment in the study, the subject may not receive study vaccine until at least 50 days after the transplant procedure). Patients undergoing MRD allogeneic HCT Patients who have not received an allogeneic HCT At least 4 months after HCT, either autologous or allogeneic (of any source, with any preparatory regimen, for any indication), prior to study treatment. Evidence of active malignancy at the time of HCT or at any time since the HCT. History of malignancy (other than the disease that required the HCT) within 5 years prior to screening. Scheduled to receive an autologous HCT Did not receive an allogeneic HCT at Dana-Farber Patient previously received allogeneic bone marrow or stem cell transplantation. Prior bone marrow or peripheral blood stem cell transplantation within the last 6 (six) months Extensive prior radiotherapy on more than 30% of bone marrow reserves, or prior bone marrow/stem cell transplantation within 5 years of study start. Extensive prior radiotherapy on more than 30% of bone marrow reserves or prior bone marrow/stem cell transplantation within 2 years before screening. Limited field radiation for ?2 weeks prior to screening period is permitted Prior bone marrow or stem cell transplantation, or radiation therapy in more than 35% of bone marrow. Participants must be designated to undergo reduced intensity allogeneic peripheral blood (PB) or bone marrow (BM) hematopoietic stem cell transplantation. Consent will be obtained prior to admission for HCT History of organ, bone marrow, or stem cell transplantation DONOR: Has undergone solid organ, stem cell, bone marrow or blood transplantation Prior allogeneic bone marrow or peripheral blood stem cell transplantation Prior hematopoietic stem cell or bone marrow transplantation Extensive prior radiotherapy, more than 30% of bone marrow reserves, or prior bone marrow/stem cell transplantation. Extensive prior RT on ?30% of bone marrow reserve as judged by the investigator or prior bone marrow/stem cell transplantation within 5 years before trial start. Prior hematopoietic stem cell or bone marrow transplantation Extensive prior radiotherapy, more than 30% of bone marrow reserves, or prior bone marrow/stem cell transplantation. History of bone marrow or stem cell transplantation (allogeneic or autologous) Patients with a history of histologically or pathologically confirmed diagnosis of AML and < 5% blasts in the peripheral blood or bone marrow (per bone marrow aspiration and/or biopsy within 6 weeks prior to screening) scheduled to undergo allogeneic stem cell transplantation Patients with a histologically or pathologically confirmed diagnosis of MDS with < 10% blasts in the bone marrow (per bone marrow aspiration and/or biopsy within 6 weeks prior to screening) scheduled to undergo allogeneic stem-cell transplantation Prior hematopoietic stem cell or bone marrow transplantation Prior hematopoietic stem cell or bone marrow transplantation. Extensive prior radiotherapy on more than 30 percent of bone marrow reserves, or prior bone marrow/stem cell transplantation within 5 years from enrolment Prior bone marrow or stem cell transplantation Prior hematopoietic stem cell or bone marrow transplantation History of bone marrow, stem cell, or allogenic organ transplantation Eligible for allogeneic bone marrow or stem cell transplantation Prior stem cell or bone marrow transplantation Patients previously treated with autologous or allogeneic bone marrow or stem cell transplantation are ineligible Extensive prior radiotherapy to more than 30% of bone marrow reserves, or prior bone marrow/stem cell transplantation. Patients previously treated with allogeneic bone marrow or stem cell transplantation are ineligible Prior allogeneic bone marrow or peripheral blood stem cell transplantation History of previous bone marrow and/or stem cell transplantation. Prior bone marrow/hematopoietic stem cell transplantation History of receiving high-dose chemotherapy requiring bone marrow or stem cell support History of previous bone marrow and/or stem cell transplantation. Prior hematopoietic stem cell or bone marrow transplantation Previous allogenic stem cell or allogeneic bone marrow transplantation History of allogeneic bone marrow or stem cell transplantation Extensive prior RT on more than 30 percent of bone marrow reserves (by Investigator judgment), or prior bone marrow/stem cell transplantation within 5 years before study start Prior organ transplantation including allogenic stem cell transplantation No prior history of organ transplantation or brain metastasis History of organ transplantation including previous history of liver transplantation Has had prior liver or other organ transplantation History of organ transplantation EXCLUSION - DURVALUMAB DRUG-SPECIFIC: History of allogenic organ transplantation. Prior organ transplantation including allogenic stem-cell transplantation History of allogenic organ transplantation. Receipt of any organ transplantation requiring ongoing immunosuppression Prior organ transplantation including allogenic stem-cell transplantation within 3 months prior to planned enrollment. Prior organ transplantation including allogenic stem-cell transplantation Patients who have had a liver or any organ transplantation History of allogenic organ transplantation that requires ongoing use of immunosuppressive agents is NOT permitted Prior organ transplantation including allogenic stem-cell transplantation. Prior organ transplantation including allogenic stem-cell transplantation Prior organ transplantation including allogenic stem-cell transplantation Prior organ transplantation History of organ transplantation History of allogenic organ transplantation History of organ transplantation History of allogenic organ transplantation that requires use of immunosuppressive agents. History of organ transplantation Receipt of any organ transplantation Prior organ transplantation including allogenic stem-cell transplantation. History of allogenic organ transplantation (both solid organ and bone marrow) History of organ transplantation History of allogenic organ transplantation History of organ transplantation History of organ transplantation History of organ transplantation History of major organ transplantation History of major organ transplantation Prior organ transplantation including allogenic stem cell transplantation. Subject has had or has planned to receive any organ transplantation; History of organ transplantation. Prior organ transplantation including allogenic stem-cell transplantation. History of organ transplantation Patient must have no history of organ transplantation or ongoing immunosuppressant therapy Prior organ transplantation including allogenic stem-cell transplantation Had organ transplantation History of any organ transplantation End-organ function not appropriate for transplantation History of organ transplantation. History of organ transplantation Participant who has a history of organ transplantation. Prior organ transplantation History of major organ transplantation with an existing functional graft Individual with history of any organ transplantation