Prior autologous or allogeneic HCTXx_NEWLINE_xXCRITERIA FOR ALLOGENEIC TRANSPLANTATIONXx_NEWLINE_xXAllogeneic stem cell transplantation is allowed provided the patient is >= 1 year from transplant at time of registration, is not on immunosuppressive therapy to treat/prevent graft-versus-host disease, has no evidence of active graft versus host disease, and no evidence of active infectionXx_NEWLINE_xXPatient must be deemed eligible to proceed with high-dose chemotherapy and autologous stem cell transplantation by local transplant centerXx_NEWLINE_xXAt least 6 weeks from autologous stem cell transplantationXx_NEWLINE_xXAt least 3 months from allogeneic stem cell transplantation and off immunosuppression and no evidence of graft versus host disease (GVHD)Xx_NEWLINE_xXPatient previously received allogeneic bone marrow or stem cell transplantation.Xx_NEWLINE_xXPrior history of allogeneic stem cell transplantationXx_NEWLINE_xXMust be ineligible for high dose therapy/ stem cell transplantationXx_NEWLINE_xXParticipants 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 transplantationXx_NEWLINE_xXHas a history of having undergone allogeneic stem cell transplantation, or any other allogeneic or xenogeneic transplantXx_NEWLINE_xXAutologous stem cell transplantation (SCT) within 100 days prior to first infusionXx_NEWLINE_xXActive or history of any serious autoimmune disease, prior organ transplantation, including allogeneic stem-cell transplantation or immune-deficiencies that required treatment with systemic immunosuppressive drugs and could flare-up during study treatment\r\n* (NOTE: Patients with diabetes type I, vitiligo, psoriasis, or hypo- or hyperthyroid diseases not requiring immunosuppressive treatment are eligible)Xx_NEWLINE_xXEligible for Autologous Hematopoietic stem cell transplantation according at the investigator discretion.Xx_NEWLINE_xXPrevious history of autologous or allogeneic-HCTXx_NEWLINE_xXPrior allogeneic stem cell transplantation with active graft-versus-host-disease.Xx_NEWLINE_xXB-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 transplantationXx_NEWLINE_xXPrior allogeneic stem-cell transplantation (SCT)Xx_NEWLINE_xXPatients who received Allo-Stem cell Transplantation(Allo-SCT) within 12 months.Xx_NEWLINE_xXPlanning to receive or have received autologous stem cell transplantation (ACST) per institutional standards as part of standard of care\r\n* Pre-ASCT participants may consent but will not be eligible to begin treatment until after ASCT, and will have to fulfill all inclusion and exclusion criteria before starting protocol\r\n* All participants must initiate day 1 of protocol therapy within 30-60 days post stem cell reinfusion; study PI can grant exception for a patient to start as late as 75 days post stem cell reinfusion with a reasonable justification for a delay (e.g. recovery from post -ASCT toxicity) and this will not be a protocol deviation, nor require an exception to be filledXx_NEWLINE_xXPatients with history of allogeneic stem cell transplantationXx_NEWLINE_xXFor 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 transplantationXx_NEWLINE_xXPrior allogeneic stem-cell transplantation (SCT), or autologous SCT within 100 days prior to Day 1 of Cycle 1Xx_NEWLINE_xXMust not be eligible for high-dose therapy with autologous stem cell transplantation rescueXx_NEWLINE_xXParticipants must be recipients of an allogeneic bone marrow or stem cell transplantation with myeloablative or reduced intensity conditioning regimensXx_NEWLINE_xXPrevious hematopoietic stem cell transplantation; patients can have had prior relapsed disease as long as they have never been previously transplantedXx_NEWLINE_xXInstitutional criteria for and have institutional approval to undergo autologous peripheral blood stem cell transplantationXx_NEWLINE_xXSubjects for whom there is the prospect of stem cell transplantation in the next 6 months in the treatment plan are excluded (including subjects for whom the PdC regimen is being considered as pre-transplant cytoreduction)Xx_NEWLINE_xXPrior allogeneic or autologous HCT at any time.Xx_NEWLINE_xXHas undergone prior allogeneic hematopoietic stem cell transplantation within the last 5 years. (Note: Participants who have had a stem cell transplant >5 years ago are eligible as long as there are no symptoms of graft-versus-host disease [GVHD].)Xx_NEWLINE_xXFor lymphoma patients only: Participants must have received and relapsed after autologous stem cell transplantation (ASCT), or be ineligible for ASCT (including on the basis of refractory disease), or have declined ASCTXx_NEWLINE_xXPrior bone marrow or peripheral blood stem cell transplantation within the last 6 (six) monthsXx_NEWLINE_xXNOTE: 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 eligibleXx_NEWLINE_xXPatients 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 transplantationXx_NEWLINE_xXPatients with a history of allogeneic stem cell transplantation are eligible for study participation provided the transplant was > 100 days prior to the first dose of treatment on study; patients must be off of immunosuppressive therapies for at least 4 weeks prior to the first dose of treatment on study without signs or symptoms of graft versus host disease other than grade 1 skin involvementXx_NEWLINE_xXSubjects with prior autologous and allogeneic hematopoietic stem cell transplantation (allo HSCT) are eligible.Xx_NEWLINE_xXSubject has active clinically significant graft versus host disease (GVHD) or is on treatment with systemic corticosteroids for GVHD (except grade 1 skin GVHD). At least 3 months must have elapsed since completion of allogeneic stem cell transplantation.Xx_NEWLINE_xXHas undergone prior allogeneic hematopoietic stem cell transplantation within the last 5 years.Xx_NEWLINE_xXHas ever received or is scheduled to receive an Allogeneic Hematopoietic Stem Cell Transplantation (alloHSCT)Xx_NEWLINE_xXPatients who have ever received an Autologous Hematopoietic Stem Cell Transplantation (autoHSCT) ARE eligible.Xx_NEWLINE_xXPatients who are scheduled to receive an Autologous Hematopoietic Stem Cell Transplantation (autoHSCT) are NOT eligibleXx_NEWLINE_xXHas failed to respond to, relapsed following, not eligible for, or opted not to participate in allogeneic stem cell transplantationXx_NEWLINE_xXSuitable 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 foundXx_NEWLINE_xXReceipt of any organ transplantation including autologous or allogeneic stem-cell transplantation.Xx_NEWLINE_xXHematological 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.Xx_NEWLINE_xXAny patients eligible for allogeneic stem cell transplantation (allo-SCT) and willing to undergo allo-SCT as determined at time of screening for trial; patients who are ineligible or not interested in undergoing allo-SCT will be eligible for the trialXx_NEWLINE_xXPatients who have undergone stem cell transplantation (SCT), autologous or allogeneic, are eligible provided that they are >= 8 weeks from stem cell infusion, have no active graft versus host disease (GVHD), are off immune suppression for at least 2 weeks, and do not have a history of veno-occlusive disease (VOD)Xx_NEWLINE_xXAdult male and female subjects at least 18 years of age who have had allogenic bone marrow transplant (BMT) or hematopoietic stem cell transplantation (HSCT).Xx_NEWLINE_xXPrior allogeneic hematopoietic stem cell transplantation (allo HSCT)Xx_NEWLINE_xXPatients who are candidates for allogeneic stem cell transplantation.Xx_NEWLINE_xXPrior allogeneic stem cell transplantation (SCT), or autologous SCT within 100 days prior to Day 1 of Cycle 1Xx_NEWLINE_xXOther high-risk hematologic malignancies eligible for stem cell transplantation per institutional standardXx_NEWLINE_xXPatients who have had an allogeneic hematopoietic stem cell transplantation are not eligible.Xx_NEWLINE_xXPatients with history of allogeneic stem cell transplantation are eligible if at least 100 days post-transplant, if there is no evidence of active graft versus host disease (GVHD) and no longer taking immunosuppressive agents for at least 30 days prior to enrollmentXx_NEWLINE_xXPrior stem-cell transplantation (SCT).Xx_NEWLINE_xXMust have undergone an allogeneic SCT (regardless of stem cell source)Xx_NEWLINE_xXPatient has an appropriate donor identified for hematopoietic stem cell transplantationXx_NEWLINE_xXDeemed eligible for autologous stem cell transplantation (ASCT) by standard institutional criteriaXx_NEWLINE_xXPrior allogeneic stem cell transplantation (SCT) is an exclusion only if the subject has active graft vs host disease or requires immunosuppression other than a constant stable dose of glucocorticoids (the latter is permitted)Xx_NEWLINE_xXHas undergone prior allogenic hematopoietic stem cell transplantation.Xx_NEWLINE_xXAUTOLOGOUS 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 apheresisXx_NEWLINE_xXPrior allogenic hematopoietic stem cell transplantation.Xx_NEWLINE_xXReceipt of any organ transplantation, including allogeneic stem-cell transplantation, but with the exception of transplants that do not require immunosuppression (e.g., corneal transplant, hair transplant).Xx_NEWLINE_xXFor 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 eligibleXx_NEWLINE_xXWill undergo first allogeneic hematopoietic stem cell transplantation (HSCT) for their malignancy. Conditioning may have been either conventional myeloablative (MAC) or reduced intensity conditioning (RIC)Xx_NEWLINE_xXPrior allogeneic stem cell transplantation with active graft-versus-host- diseaseXx_NEWLINE_xXPatients who are candidates for allogeneic transplantation, have a suitable donor, and are willing to undergo transplantationXx_NEWLINE_xXRelapsed patients who have undergone autologous or allogeneic hematopoietic stem cell transplantation previouslyXx_NEWLINE_xXPatients with psychological or medical condition that patient's physician deems unacceptable to proceed to allogeneic hematopoietic stem cell transplantationXx_NEWLINE_xXHigh risk prediction score as determined by the Mount Sinai Acute Graft Versus Host Disease (GVHD) International Consortium (MAGIC) algorithm at either day 7 or day 14 post hematopoietic stem cell transplantation (HCT).Xx_NEWLINE_xXReceipt of any organ transplantation, including allogeneic stem-cell transplantation, except of transplants that do not require immunosuppression (e.g., corneal transplant, hair transplant)Xx_NEWLINE_xXPatients with history of allogeneic stem cell transplantation are eligible if at least 100 days post-transplant, if there is no evidence of active GVHD and no longer taking immunosuppressive agents for at least 30 days prior to enrollmentXx_NEWLINE_xXPrior allogeneic stem cell transplantationXx_NEWLINE_xXCohort #1: considered eligible for high-dose chemotherapy followed by autologous stem cell transplantation (ASCT)Xx_NEWLINE_xXReceipt of any organ transplantation, including allogeneic stem-cell transplantation, but with the exception of transplants that do not require immunosuppression (e.g., corneal transplant, hair transplant).Xx_NEWLINE_xXAge-adjusted hematopoietic cell transplantation-comorbidity index (aaHCT-CI) less than or equal to 7.Xx_NEWLINE_xXParticipants 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 HCTXx_NEWLINE_xXSubject is a candidate for hematopoietic stem cell transplantation (HSCT).Xx_NEWLINE_xXIn subjects with prior hematopoietic progenitor cell transplantation, evidence of ongoing graft-versus-host disease (GVHD).Xx_NEWLINE_xXHas undergone solid organ transplant at any time, or prior allogeneic hematopoietic stem cell transplantation within the last 5 yearsXx_NEWLINE_xXHistory of corneal transplantationXx_NEWLINE_xXPatients with a prior autologous or allogeneic HCTXx_NEWLINE_xXPatients with a history of prior hematopoietic stem cell transplantation (HSCT), elevated conjugated serum bilirubin at study entry, uncontrolled systemic fungal, bacterial, or other infection, a history of hepatitis B or C infection or a history of cirrhosisXx_NEWLINE_xXHigh-dose chemotherapy followed by stem cell transplantation (autologous or allogeneic).Xx_NEWLINE_xXPrior autologous or allogeneic stem cell transplantationXx_NEWLINE_xXPrior allogeneic stem cell or organ transplantation including corneal transplantXx_NEWLINE_xXHave received a T cell-depleted allogeneic (i.e., non-autologous) HCT within the previous 100 days.Xx_NEWLINE_xXPatient has had a prior autologous or allogeneic HSCT.Xx_NEWLINE_xXPatients who in the opinion of the treating physician are unlikely to comply with the restrictions of allogeneic stem cell transplantation based on formal psychosocial screeningXx_NEWLINE_xXRelapse after allogeneic stem cell transplantation prior to post-transplant day 30Xx_NEWLINE_xXReceipt of any organ transplantation, including allogeneic stem-cell transplantation, but with the exception of transplants that do not require immunosuppression (e.g. corneal transplant, hair transplant)Xx_NEWLINE_xXPrior organ transplantation including allogeneic stem cell transplantation, brain metastases (except those meeting certain protocol specified criteria which are acceptable), significant acute or chronic infections, a history of cardiovascular/cerebrovascular disease.Xx_NEWLINE_xXHigh dose chemotherapy followed by autologous stem cell transplantation within 90 days prior to initiating study treatment;Xx_NEWLINE_xXHas undergone prior allogeneic hematopoietic stem cell transplantation within the last 5 years. (Subjects who have had a transplant greater than 5 years ago are eligible as long as there are no symptoms of graft versus host disease (GVHD).Xx_NEWLINE_xXIs 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:Xx_NEWLINE_xXHas a history of allogeneic stem cell transplantationXx_NEWLINE_xXPrior 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 timeXx_NEWLINE_xXSubjects who have opted not to undergo allogeneic hematopoietic stem cell transplantation and who are not deemed eligible for high intensity chemotherapy.Xx_NEWLINE_xXPrior history of allogeneic hematopoietic stem cell transplantation.Xx_NEWLINE_xXSubjects 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 daysXx_NEWLINE_xXHas a history of allogeneic stem cell transplantationXx_NEWLINE_xXImmunosuppression following a Hematopoietic Stem Cell Transplantation (HSCT) within 6 weeks prior to study entry;Xx_NEWLINE_xXPrior stem cell transplantation for myelomaXx_NEWLINE_xXPrior organ transplantation including allogeneic stem-cell transplantsXx_NEWLINE_xXPatients 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 transplantXx_NEWLINE_xXAllogeneic hematopoietic cell transplantation within 5 years of study drug administrationXx_NEWLINE_xXPatients with HL or DLBCL must refuse or not be candidates for curative autologous stem cell transplantationXx_NEWLINE_xXAcceptable allogeneic stem cell donor with imminent plans to proceed with allo-SCT.Xx_NEWLINE_xXAllogeneic hematopoietic stem cell transplantation (HSCT) within 24 weeks before the start of protocol-specified therapy.Xx_NEWLINE_xXPHASE I: Patients who underwent an allogeneic hematopoietic stem cell transplantation from any donor source for acute lymphocytic leukemiaXx_NEWLINE_xXPHASE I: Patients who are between T+40 and T+100 after allogeneic transplantationXx_NEWLINE_xXPHASE I: Patients who have evidence of donor chimerism after allogeneic transplantationXx_NEWLINE_xXPHASE II: Patients who underwent an allogeneic hematopoietic stem cell transplantation from any donor source for acute lymphocytic leukemiaXx_NEWLINE_xXPHASE II: Patients who are between T+40 and T+100 after allogeneic transplantationXx_NEWLINE_xXPHASE II: Patients who have >= 80% donor chimerism after allogeneic transplantationXx_NEWLINE_xXPrior history of stem cell transplantationXx_NEWLINE_xXPrior allogeneic stem cell transplantation (ASCT) or other anti-CD22 immunotherapy within =< 4 months before first dose of study treatmentXx_NEWLINE_xXAML relapse > 6 months since autologous or allogeneic stem cell transplantation, provided there is no active graft-versus-host disease (GVHD) > grade 1; no treatment with high dose steroids for GVHD (up to 20 mg prednisolone or equivalent); no treatment with immunosuppressive drugs with the exception of low dose cyclosporine and tacrolimus (blood levels of 0.5-0.6 ug/mL)Xx_NEWLINE_xXEither not eligible or unwilling to proceed with hematopoietic stem cell transplantation (HSCT)Xx_NEWLINE_xXEligible for, have a suitable donor, and are willing to undergo hematopoietic stem cell transplantation (HSCT)Xx_NEWLINE_xXPatients with aggressive NHL must have failed autologous hematopoietic stem cell transplantation (HSCT), or are ineligible or not consenting to autologous HSCTXx_NEWLINE_xXPrior allogeneic bone marrow or peripheral blood stem cell transplantationXx_NEWLINE_xXPrior autologous bone marrow or peripheral blood stem cell transplantation =< 100 days prior to registration or if recovery from the transplant is inadequateXx_NEWLINE_xXReceived prior autologous stem cell transplantation as first line therapy for multiple myeloma with subsequent disease relapse/progressionXx_NEWLINE_xXCandidate 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 transplantationXx_NEWLINE_xXMore than one prior transplant prior to study entry with the exception of tandem transplantation; tandem transplantation is defined as two autologous stem cell transplants that occur within 9 months of one another, and the patient did not have disease progression in the period between the two transplantsXx_NEWLINE_xXMeets one of the following disease criteria:\r\n* Multiple myeloma (MM) meeting one of the following:\r\n** Relapsed/refractory disease after two lines of therapies, including a proteasome inhibitor (bortezomib, carfilzomib or ixazomib) and an immunomodulatory drug (thalidomide, lenalidomide or pomalidomide)\r\n** Relapsed disease between 2-18 months of 1st autologous stem cell transplantation\r\n** Relapsed disease at least 4 months after allogeneic stem cell transplantation with no evidence of active graft versus host disease AND with measurable disease defined as serum IgG, A, M M-protein >= 0.5 g/dL or serum IgD M-protein >= 0.5 g/dL, or urine M-protein >= 200 mg/24 hours AND at least at least 4 weeks since plasmapheresis\r\n* CD20-positive B-cell non-Hodgkin lymphoma (NHL)\r\n** CD20 expression confirmed by flow cytometry or immunohistochemistry and meeting one or more of the following:\r\n** Evidence of relapsed/refractory disease that has failed conventional therapy\r\n** Relapsed disease at least 60 days after autologous stem cell transplantation\r\n** Relapsed disease at least 4 months after allogeneic stem cell transplantation with no evidence of active graft versus host disease\r\n** Has measurable disease > 1.5 cm in diameterXx_NEWLINE_xXPrior autologous or allogeneic stem cell transplantationXx_NEWLINE_xXPrior treatment with chimeric antigen receptor (CAR) T cells or other forms of adoptive cellular therapy, with the exception of autologous stem cell transplantationXx_NEWLINE_xXMust have undergone allogeneic hematopoietic stem cell transplantation (HSCT) (regardless of stem cell source)Xx_NEWLINE_xXHistory of prior autologous hematopoietic cell transplantationXx_NEWLINE_xXHistory of corneal transplantationXx_NEWLINE_xXPrior hematopoietic transplantation is allowed (autologous and/or allogeneic)Xx_NEWLINE_xXPrior stem cell transplantationXx_NEWLINE_xXPatients diagnosed with acute myeloid leukemia (AML) by World Health Organization (WHO) classification, meeting one of following criteria:\r\n* Age 60 or older, newly diagnosed, untreated, who are unwilling to undergo or not candidates for conventional induction chemotherapy with cytarabine/anthracyclines\r\n* Age 60 or older with relapsed or refractory disease\r\n* Younger adult patients with previously untreated high-risk disease (complex karyotype, inv[3] or t[3;3], t[6;9], monosomal karyotype, therapy-related and secondary disease) that are unwilling to undergo or not candidates for conventional induction chemotherapy with cytarabine/anthracyclines and/or allogeneic stem cell transplantation\r\n* Younger patients with refractory/relapsed AML who are otherwise not candidates for allogeneic stem cell transplantation\r\n* Patients with extramedullary disease who meet one of the above criteria may be includedXx_NEWLINE_xXRecipients of allogeneic stem cell transplantation with myeloablative or non-myeloablative conditioning regimens; alternative donor transplants (umbilical cord blood and haploidentical) are allowedXx_NEWLINE_xXAutologous stem cell transplantation within 12 weeks before the starting IP treatment or past history of allogeneic stem cell transplantation.Xx_NEWLINE_xXHas undergone prior allogeneic hematopoietic stem cell transplantation within the last 5 yearsXx_NEWLINE_xXHematological 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.Xx_NEWLINE_xXPatients with prior autologous or allogeneic hematopoietic cell transplantation (HCT) are eligible if relapse occurs provided symptoms of graft-versus host disease are well controlled with stable use of immunosuppressive agentsXx_NEWLINE_xXPrevious allogeneic hematopoietic stem cell transplantationXx_NEWLINE_xXPatients who have had prior SCT are eligible if they have a relapse > 3 months since autologous or allogeneic stem cell transplantation provided, 1) no clinically significant active graft-versus-host disease (GVHD > grade 1); 2) no treatment with high dose steroids for GVHD (i.e. > 20 mg prednisolone or equivalent per day); 3) no treatment with immunosuppressive drugs with the exception of cyclosporine and tacrolimusXx_NEWLINE_xXPatients with any of the following hematologic malignancies who are considered to be eligible for allogeneic transplantation:Xx_NEWLINE_xXPatient participants who have undergone autologous stem cell transplantation (autoSCT) are eligible provided that they are >= 4 weeks from stem cell infusionXx_NEWLINE_xXPatient participants who have undergone allogeneic SCT (alloSCT) are eligible if they are >= 60 days from stem cell infusion, have no evidence of graft versus host disease (GVHD) > grade 1, and are >= 2 weeks off all immunosuppressive therapyXx_NEWLINE_xXPatients are planned for treatment with high dose melphalan and autologous hematopoietic cell transplantation (HCT)Xx_NEWLINE_xXPrior history of allogeneic hematopoietic cell transplantationXx_NEWLINE_xXAutologous stem cell transplantation within 12 weeks prior to study entryXx_NEWLINE_xXHave undergone allogeneic stem cell transplantationXx_NEWLINE_xXRelapsed after allogeneic transplantationXx_NEWLINE_xXPrior autologous or allogeneic HCTXx_NEWLINE_xXNo plan for allogeneic stem cell transplantation within 3 monthsXx_NEWLINE_xXPrior hematopoietic transplantation is allowed (autologous and/or allogeneic)Xx_NEWLINE_xXPrior hematopoietic stem cell or bone marrow transplantationXx_NEWLINE_xXChronic graft-versus-host disease requiring systemic immunosuppression post-allogeneic hematopoietic stem cell transplantationXx_NEWLINE_xXRESEARCH SAMPLE COLLECTION: Considered for high-dose melphalan followed by autologous hematopoietic cell transplantation and undergoing pre-HCT workupXx_NEWLINE_xXDiagnosis of multiple myeloma undergoing planned autologous stem cell transplantationXx_NEWLINE_xXPatients 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 weeksXx_NEWLINE_xXCohort 2: Persistence or reappearance of minimal residual disease by flow cytometry or cytogenetic or molecular testing while being in morphological remission after allogeneic stem cell transplantationXx_NEWLINE_xXCohort 3: High risk AML and MDS patients who are in complete remission morphologically with no evidence of minimal residual disease by flow cytometry or cytogenetic or molecular testing after allogeneic stem cell transplantationXx_NEWLINE_xXPatients must have undergone hematopoietic stem cell transplantation and have moderate to severe chronic GVHD as defined by the National Institute of Health (NIH) consensus criteriaXx_NEWLINE_xXPatients who have undergone stem cell transplantation (SCT), autologous or allogeneic, are eligible provided that they are > 60 days from stem cell infusion, have graft-versus-host disease (GVHD) =< grade 1 and are off immunosuppressive agents for > 28 days at time of registrationXx_NEWLINE_xXPatient must meet one of the following criteria: \r\n* Patient refractory to one or two standard induction regimen \r\n* Patients with a first untreated relapse within 2 years of documentation of clinical remission; patients relapsing after allogeneic stem cell transplantation are eligible if more than 12 months after transplantation and without sign of active graft versus host disease (GVHD)Xx_NEWLINE_xXPatients >= 70 and =< 75 years of age may be eligible if they have a Hematopoietic Cell Transplantation- Comorbidity Index (HCT-CI) Co-Morbidity score =< 2Xx_NEWLINE_xXNot suitable for, or declined high dose chemotherapy and autologous stem cell transplantation (ASCT).Xx_NEWLINE_xXPrior hematopoietic allogenic stem cell transplantation.Xx_NEWLINE_xXPrior autologous stem cell transplantation.Xx_NEWLINE_xXPatients with prior autologous and allogeneic hematopoietic stem cell transplantation are eligible if patients are off immunosuppression for greater than 14 days and have no evidence of active graft versus host disease (GVHD) except grade 1 skin GVHDXx_NEWLINE_xXPatients 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 lessXx_NEWLINE_xXPatients 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 therapyXx_NEWLINE_xXRelapsed or refractory B-cell ALL:\r\n* 1st or greater bone marrow (BM) relapse OR\r\n* Any marrow relapse after allogeneic hematopoietic stem cell transplantation (HSCT) and > 100 days from transplant OR\r\n* For patients with refractory disease:\r\n** < 60 years old that have not achieved a complete remission (CR) after > 2 or more chemotherapy regimens\r\n** >= 60 years old that have not achieved a CR after 1 prior chemotherapy regimenXx_NEWLINE_xXSubjects must not have undergone allogeneic stem cell transplantationXx_NEWLINE_xXPrior treatment with allogeneic stem cell transplantationXx_NEWLINE_xXPrior hematopoietic stem cell or bone marrow transplantationXx_NEWLINE_xXHave undergone organ transplantation including allogeneic or autologous stem-cell transplantation, at any time;Xx_NEWLINE_xXHas undergone prior allogeneic hematopoetic stem cell transplantation within the last 5 yearsXx_NEWLINE_xXPatients who have undergone allogeneic stem cell transplantationXx_NEWLINE_xXPatients who have undergone autologous stem cell transplantation within 3 months from study entryXx_NEWLINE_xXTandem autologous transplantationXx_NEWLINE_xXIndividuals 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 availableXx_NEWLINE_xXPatients who have undergone prior autologous stem cell transplantation or allogeneic transplantationXx_NEWLINE_xXStudy enrollment no earlier than 3 months after preceding hematopoietic cell transplantation (HSCT)Xx_NEWLINE_xXDONOR SELECTION: Not applicable; this protocol employs autologous transplantation, utilizing the patient’s own hematopoietic stem cells obtained from either the peripheral blood or bone marrowXx_NEWLINE_xXPatients 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 transplantationXx_NEWLINE_xXPatients who have poor or no graft function post stem cell transplantationXx_NEWLINE_xXPatients must have undergone autologous stem cell transplantation, within 18 months of initiation of induction therapy for newly diagnosed myelomaXx_NEWLINE_xXFirst allogeneic hematopoietic stem cell transplantation (HSCT) using myeloablative conditioning (MAC), non-myeloablative (NMA), or reduced-intensity conditioning (RIC) preparative regimens.Xx_NEWLINE_xXRelapse > 6 months since autologous or allogeneic stem cell transplantation provided:\r\n* No active graft-versus-host disease (GVHD > grade 1)\r\n* No treatment with high dose steroids for GVHD (up to >= 20 mg prednisolone or equivalent per day)\r\n* No treatment with immunosuppressive drugs with the exception of low dose cyclosporine and tacrolimusXx_NEWLINE_xXAllogeneic stem cell transplantation within 6 months, or has active GVHD requiring ongoing immunosuppression.Xx_NEWLINE_xXPrior high dose chemotherapy for autologous hematopoietic cell transplantation or prior allogeneic transplantationXx_NEWLINE_xXPrior allogeneic or autologous transplantationXx_NEWLINE_xXPrior allogeneic stem cell transplantationXx_NEWLINE_xXPatients must have an allogeneic hematopoietic progenitor cell donor (HPCT), either a matched sibling, mismatched (1 allele) sibling, or a matched unrelated donor (MUD) or a mismatched (1 allele) unrelated donor\r\n* Previous autologous hematopoietic progenitor cell transplantation is allowed; a minimum of 6 months should have elapsed from prior autologous hematopoietic progenitor cell transplantation; prior transplantation with conditioning regimens using total body irradiation is not allowedXx_NEWLINE_xXPrior allogeneic hematopoietic progenitor cell transplantationXx_NEWLINE_xXPrior autologous hematopoietic progenitor cell transplantation if the conditioning regimen included total body irradiationXx_NEWLINE_xXHematopoietic Cell Transplantation-Specific Comorbidity Index score (HCT-CI) =< 4 for patients in Cohort 1 and > 4 for Cohort 2Xx_NEWLINE_xXTransplantation for AML (allogeneic or autologous) allowed unless within 90 days of study entryXx_NEWLINE_xXPatients with psychological or medical condition that patient's physician deems unacceptable to proceed to allogeneic hematopoietic stem cell transplantationXx_NEWLINE_xXPatients should have received single autologous stem cell transplantation 60-120 days prior to enrollment to the trialXx_NEWLINE_xXDIAGNOSIS 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 ORXx_NEWLINE_xXRelapsed after allogeneic transplantationXx_NEWLINE_xXPatients must be eligible to undergo autologous stem cell transplantation by standard institutional criteriaXx_NEWLINE_xXPatients with relapsed or primary refractory AML; patients with relapsed AML after allogeneic stem cell transplantation, including those who have received donor lymphocyte infusions, are eligible if they have no active graft versus host disease (GVHD) and are off immunosuppressionXx_NEWLINE_xXPatients having undergone prior allogeneic stem cell transplantation within 6 months or having active graft versus host disease.Xx_NEWLINE_xXPatients with B-cell hematological malignancies who are eligible for allogeneic transplantationXx_NEWLINE_xXHistory of bone marrow or stem cell transplantation (allogeneic or autologous)Xx_NEWLINE_xXPrior allogeneic marrow or stem cell transplantation.Xx_NEWLINE_xXAt least 60 days from day of transplantationXx_NEWLINE_xXMalignant conditions for which CD34+ selected, T-cell depleted allogeneic hematopoietic stem cell transplantation is indicated such as:Xx_NEWLINE_xXPrior high dose chemotherapy with autologous stem cell transplant, or prior allogeneic transplantationXx_NEWLINE_xXPatients 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 regimenXx_NEWLINE_xXHistory of CD19+ malignancy with evidence of relapse or persistent minimal residual disease (MRD) following autologous or allogeneic hematopoietic stem cell transplantation (cohort 1)\r\n* Relapse on this protocol is detection of CD19+ malignancies in bone marrow (>= 5%) or extramedullary lesion by morphology, cytogenetics, molecular, radiographic, and/or flow cytometry\r\n* Persistent minimal residual disease after transplantation must be demonstrated by morphology, karyotype, fluorescent in situ hybridization (FISH), flow cytometry, or reverse transcriptase (RT)-polymerase chain reaction (PCR)Xx_NEWLINE_xX-  Participant is not a candidate to undergo intensive chemotherapy or allogeneic hematopoietic stem cell transplantation (HSCT).Xx_NEWLINE_xXAllowed prior allogeneic hematopoietic stem cell transplantation (allo-HCT) regardless of stem cell source; patients must be at least 3 months post allo-HCT (at time of treatment start); mismatched transplantations would be allowedXx_NEWLINE_xXMalignant 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:Xx_NEWLINE_xXMultiple 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 transplantXx_NEWLINE_xXPrior autologous or allogeneic hematopoietic cell transplantation (other than autologous SCT 60-120 days prior to registration)Xx_NEWLINE_xXMinimum donor and stem cell requirements for high-risk patients undergoing stem cell transplantation:Xx_NEWLINE_xXPatients 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 diseaseXx_NEWLINE_xXPatients eligible for hematopoietic stem cell transplantationXx_NEWLINE_xXPatients considered for transplantation must have a sufficient graft as based on current criteria of the University of Minnesota Blood and Marrow Transplantation ProgramXx_NEWLINE_xXTime available (at least 12 weeks) for treatment of hepatitis C prior to autologous or allogeneic transplantationXx_NEWLINE_xX>=6 months after completing any line of chemotherapy, or after autologous stem cell transplantation, and having attained either a very good partial response (VGPR) or a complete response (CR), and without the need for haematological maintenance therapies Inclusion Criteria for Group 3Xx_NEWLINE_xXLess than 3 months since received hematopoietic stem cell transplantation, autologous or allogeneic and/or have clinically significant graft versus-host disease requiring treatment at the time of screening and/or patient having a history of severe graft versus-host disease;Xx_NEWLINE_xXPatients who have received prior allogeneic stem cell-transplantationXx_NEWLINE_xXPatients who have undergone a stem cell transplantation.Xx_NEWLINE_xXPatients who have had a prior stem cell transplantation are NOT eligible for participationXx_NEWLINE_xXPrior autologous or allogeneic transplantation for any diseaseXx_NEWLINE_xXLess than 2 months following bone marrow or peripheral blood stem cell transplantation or treatment with donor lymphocyte infusion (DLI).Xx_NEWLINE_xXPrior hematopoietic stem cell or bone marrow transplantationXx_NEWLINE_xXAutologous stem cell transplantation less than 90 days prior to study day 1Xx_NEWLINE_xXHistory of organ or previous autologous/allogeneic stem cell transplantationXx_NEWLINE_xXNo 10/10 matched sibling donor available or not financially eligible for allogeneic stem cell transplantationXx_NEWLINE_xXHas received allogeneic hematopoietic cell transplantation (HSCT) within 3 months of planned infusion of genetically modified T cells; HSCT >= 3 months from CAR-T cell infusion eligible.Xx_NEWLINE_xXPrior hematopoietic stem cell or bone marrow transplantation.Xx_NEWLINE_xXPrior hematopoietic cell transplantation allogeneic or autologous (A prior autologous HCT will be allowed as long as it was part of tandem transplantation).Xx_NEWLINE_xXPrior allogeneic hematopoietic stem cell transplantation within previous 100 daysXx_NEWLINE_xXStem cell transplantationXx_NEWLINE_xXPrior allogeneic (allo)-hematopoietic cell transplantation (HCT) less than three months from the time of enrollmentXx_NEWLINE_xXPatients 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 lessXx_NEWLINE_xXPatients 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 diseaseXx_NEWLINE_xXPatients who have received allogeneic hematopoietic stem cell transplantation are ineligibleXx_NEWLINE_xXPrior allogeneic hematopoietic cell transplantationXx_NEWLINE_xXPrevious allogeneic stem cell transplantation with active graft versus host disease (GVHD), or treatment with immunosuppressive therapy (excluding corticosteroids) in the 2 months prior to study entryXx_NEWLINE_xXSubjects who are candidates for allogeneic transplantation, have a suitable donor, and are willing to undergo transplantationXx_NEWLINE_xXMyeloablative or non-myeloablative allogeneic hematopoietic cell transplantationXx_NEWLINE_xXNo prior myeloablative therapy or hematopoietic cell transplantationXx_NEWLINE_xXHave received or are ineligible for immediate established curative regimens, including stem cell transplantationXx_NEWLINE_xXPatients who have undergone autologous stem cell transplantation (ASCT) are eligible provided that they are >= 4 weeks from stem cell infusion and meet other eligibility criteriaXx_NEWLINE_xXPatients who have undergone allogeneic SCT (alloSCT) are eligible if they are >= 60 days post stem cell infusion, have no evidence of graft-versus-host disease (GVHD) > grade 1, and are >= 2 weeks off all immunosuppressive therapyXx_NEWLINE_xXEligible for autologous transplantationXx_NEWLINE_xXPrevious stem cell collection or transplantation (autologous or allogeneic)Xx_NEWLINE_xXHistory of allogeneic stem cell transplantationXx_NEWLINE_xXPrior high-dose chemotherapy and autologous hematopoietic cell transplantation (HCT)(s) is (are) allowedXx_NEWLINE_xXPatients with history of allogeneic stem cell transplantation are eligible if at least 100 days post-transplant, if there is no evidence of active graft-versus-host disease (GVHD) and no longer taking immunosuppressive agents for at least 30 days prior to enrollmentXx_NEWLINE_xXPrior allogeneic stem cell transplantationXx_NEWLINE_xXPatients 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 enrolledXx_NEWLINE_xXPatients who have undergone autologous or allogeneic stem cell transplantationXx_NEWLINE_xXPrior allogeneic stem cell transplantationXx_NEWLINE_xXPrior autologous or allogeneic hematopoietic stem cell transplantation (HSCT)Xx_NEWLINE_xXConsidered 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 studiesXx_NEWLINE_xXRequirement of re-transplantation for primary non functionXx_NEWLINE_xXHematopoietic cell transplantation (At least 60 days from infusion of hematopoietic cells prior to first dose of tazemetostat)Xx_NEWLINE_xXHave undergone first allogeneic hematopoietic stem cell transplantation (allo-HSCT) from any donor source using bone marrow, peripheral blood stem cells, or cord blood for hematologic malignancies. Recipients of nonmyeloablative and myeloablative conditioning regimens are eligible.Xx_NEWLINE_xXCompletion of, if applicable, an autologous stem cell transplantation (ASCT) at least 3 months prior to first dose of study drug.Xx_NEWLINE_xXPrior allogeneic stem cell transplantation (SCT) within the last 5 years.Xx_NEWLINE_xXHas undergone prior allogeneic hematopoetic stem cell transplantation within the last 5 years.Xx_NEWLINE_xXAllogeneic hematopoietic stem cell transplantation within the last 5 years.Xx_NEWLINE_xXPrior allogeneic stem-cell transplantation is excluded.Xx_NEWLINE_xXNot a candidate for curative therapy or hematopoietic stem-cell transplantation (either due to disease burden, fitness, or preference).Xx_NEWLINE_xXPatients deemed clinically eligible for allogeneic stem cell transplantation.Xx_NEWLINE_xXHas undergone prior organ or allogeneic hematopoetic stem cell transplantationXx_NEWLINE_xXHas received autologous stem cell transplantation (ASCT) within 12 weeks before the date of randomization.Xx_NEWLINE_xXHas undergone prior allogeneic hematopoetic stem cell transplantation within the last 5 years. (Participants who have had a transplant greater than 5 years ago are eligible as long as there are no symptoms of Graft versus Host Disease [GVHD]).Xx_NEWLINE_xXHistologically confirmed DLBCL at last relapse(by central pathology review before enrolment. .- Relapsed or refractory disease after ?2 lines of chemotherapy including rituximab and anthracycline and either having failed autologous Hematopoietic stem cell transplantation (ASCT), or being ineligible for or not consenting to ASCTXx_NEWLINE_xXAML with antecedent hematological disease (e.g., myelodysplastic syndrome (MDS), myelofibrosis, polycythemia vera, etc.) and not a candidate for stem cell transplantation (SCT) in their current disease state.Xx_NEWLINE_xXParticipant must be ineligible or unwilling to undergo stem cell transplantation at time of study entryXx_NEWLINE_xXPrior hematopoietic stem cell transplantation within 12 weeks of the first dose of study treatment or ongoing immunosuppressive therapy for graft versus host diseaseXx_NEWLINE_xXPatients who have undergone autologous hematopoietic stem cell transplantation are eligible once they have recovered from all toxicities from therapyXx_NEWLINE_xXPatients who have received allogeneic hematopoietic stem cell transplantation will be eligible 6 months after the procedure provided there is no evidence of active graft-versus-host disease and immunosuppressive treatment has been discontinued for at least 30 days.Xx_NEWLINE_xXHave had at least 60 days between prior hematopoietic stem cell transplantation (SCT) and first dose of study drug.Xx_NEWLINE_xXAny BM relapse after allogeneic stem cell transplantation (SCT) and must be ? 6 months from SCT at the time of CTL019 infusion OR.Xx_NEWLINE_xXHematopoietic stem cell transplantation ? 4 months of dosingXx_NEWLINE_xXHistory of corneal transplantationXx_NEWLINE_xXPrior bone marrow or stem cell transplantationXx_NEWLINE_xXInability to comply with the requirements for care after allogeneic stem cell transplantationXx_NEWLINE_xXEvidence of clinically significant immunosuppression such as organ or stem cell transplantation, any severe congenital or acquired cellular and/or humoral immune deficiency, concurrent opportunistic infection.Xx_NEWLINE_xXHas undergone prior organ or allogeneic hematopoetic stem cell transplantationXx_NEWLINE_xXHas undergone prior allogeneic hematopoietic stem cell transplantation within the last 5 years. (Subjects who have had a transplant greater than 5 years ago are eligible as long as there are no symptoms of GVHD.)Xx_NEWLINE_xXPatients must NOT have received autologous or allogeneic stem cell transplantationXx_NEWLINE_xXPrior hematopoietic stem cell or bone marrow transplantationXx_NEWLINE_xXPrior allogeneic stem-cell transplantation (SCT)Xx_NEWLINE_xXhave undergone previous allogenic stem cell transplantationXx_NEWLINE_xXPrior allogeneic stem cell transplantation (SCT)Xx_NEWLINE_xXSubject who has history of organ transplant or allogeneic hematopoietic stem cell transplantation.Xx_NEWLINE_xXEligible for autologous stem cell transplantationXx_NEWLINE_xXHas received more than 1 hematopoietic stem cell transplantation.Xx_NEWLINE_xXSubjects with relapsed primary disease, or subjects who have been treated for relapse after the allogeneic hematopoietic stem-cell transplantation (allo-HSCT) was performed.Xx_NEWLINE_xXEligible for allogenic stem cell transplantation.Xx_NEWLINE_xXPatients with allogeneic stem cell transplantation within the last 6 months or patients with active graft-versus-host disease (GVHD) will be excludedXx_NEWLINE_xXPrior allogeneic stem cell transplantationXx_NEWLINE_xXFor patients with relapsed/refractory disease: patients with prior autologous or allogeneic hematopoietic cell transplantation (HCT) for MDS/AML are eligible if relapse occurs provided symptoms of graft-versus host disease are well controlled with stable use of immunosuppressive agentsXx_NEWLINE_xXThe 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 practiceXx_NEWLINE_xXEligible for allogeneic bone marrow or stem cell transplantationXx_NEWLINE_xXPrior stem cell or bone marrow transplantationXx_NEWLINE_xXPatients that have received prior allogeneic stem cell transplantation are excluded from this studyXx_NEWLINE_xXPatients must be between 2-6 months post-transplantation at the time of study registrationXx_NEWLINE_xXThe 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)Xx_NEWLINE_xXPrior stem cell transplantation allogeneic or autologousXx_NEWLINE_xXReceipt of any organ transplantation, including allogeneic stem-cell transplantation, but with the exception of transplants that do not require immunosuppression (eg, corneal transplant, hair transplant)Xx_NEWLINE_xXAutologous stem cell transplantation (SCT) within 100 days prior to study drug, or any prior allogeneic SCT or solid organ transplantationXx_NEWLINE_xXAny previous autologous hematopoietic stem cell transplantation (HSCT) must have occurred at least 3 months prior to start of conditioningXx_NEWLINE_xXDiagnosed with AML and eligible for standard induction chemotherapy or stem cell transplantationXx_NEWLINE_xXFor 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 transplantationXx_NEWLINE_xXPrior allogeneic stem cell transplantation (SCT), completion of autologous SCT within 100 days prior to Day 1 of Cycle 1 (D1C1)Xx_NEWLINE_xXEligible for autologous stem cell transplantationXx_NEWLINE_xXAML participants < 60 years old must be in second or further relapse or relapsing after allogeneic stem cell transplantation regardless of number of relapsesXx_NEWLINE_xXHas received high dose chemotherapy followed by autologous stem cell transplantation less than 90 days prior to first dose of study treatmentXx_NEWLINE_xXPrior treatment with stem cell transplantationXx_NEWLINE_xXPrior stem cell transplantation (autologous or allogeneic)Xx_NEWLINE_xXSubject underwent transplantation at least 3 months prior to enrollmentXx_NEWLINE_xXPrior allogeneic hematopoietic stem cell transplantationXx_NEWLINE_xXActive graft versus host disease (GVHD) after allogeneic stem cell transplantation; at least 2 months must have elapsed since completion of an allogeneic stem cell transplantationXx_NEWLINE_xXPrior hematopoietic stem cell transplantationXx_NEWLINE_xXParticipants 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 transplantationXx_NEWLINE_xXPatients who have received allogenic stem cell transplantation < 12 months prior to entering the study or show evidence of active graft-versus-host disease that requires immunosuppressive therapyXx_NEWLINE_xXPatients who have undergone stem cell transplantation (SCT), autologous or allogeneic, are eligible provided that they are > 84 days from stem cell infusion, have no active graft-versus-host disease (GVHD), are off immunosuppressive agents for > 14 daysXx_NEWLINE_xXResearch participant has an indication to be considered for autologous stem cell transplantationXx_NEWLINE_xXResearch 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 procedureXx_NEWLINE_xXParticipants who have had prior allogeneic stem cell transplantation with evidence of active graft-versus-host disease requiring immunosuppressive therapyXx_NEWLINE_xXThe patient has received any hematopoietic stem cell transplantation (HSCT) ? 3 months prior to start of Investigational Product.Xx_NEWLINE_xXThe patient has received allogeneic hematopoietic stem cell transplantation (HSCT) ? 3 months or autologous HSCT ? 21 days prior to start of Investigational Product (IP).Xx_NEWLINE_xXAllogeneic stem cell transplantationXx_NEWLINE_xXSubjects who relapse after allogeneic transplantation;Xx_NEWLINE_xXPatients with AML must have either: (a) relapsed or refractory leukemia after receiving at least one prior conventional induction therapy. Those in early first relapse must not have a matched donor and/or they must not be a candidate for allogeneic stem cell transplantation (usually this would mean the patient is too ill, obese, has a co-morbid condition or is over the age of 55 years) or (b) poor-risk AML as defined below: (i) Treatment related AML, except if it is associated with favorable cytogenetics (e.g., inversion 16, t(16;16), t(8;21), t(15;17), and not a candidate for stem cell transplantation, or (ii) AML with an antecedent hematologic disease (e.g., MDS, myelofibrosis, polycythemia vera, etc.), and not a candidate for stem cell transplantation. (iii) De novo AML > 70 years of age. (iv) AML with unfavorable cytogenetics regardless of age (>18 years), if patients are not candidates for allogeneic transplantation. Unfavorable cytogenetics are the following: complex (>3 abnormalities), -7, -5, 7q-, 5q-, abnormalities of 11q23 excluding t(9;11), t(9;22), inversion 3, t(3;3), t(6;9). (c) Patients older than 60 years of age who had AML (i.e., > 20% bone marrow blasts) and no prior therapy for AMLXx_NEWLINE_xXPrior allogeneic stem cell transplantationXx_NEWLINE_xXPatients 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:Xx_NEWLINE_xXPatient is considered for autologous stem cell transplantation with full dose melphalan (200 mg/m^2)Xx_NEWLINE_xXPatients previously treated with autologous or allogeneic bone marrow or stem cell transplantation are ineligibleXx_NEWLINE_xXPatients 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 diagnosisXx_NEWLINE_xXRecipients of prior allogeneic hematopoietic stem cell transplantationXx_NEWLINE_xXPatient must have undergone autologous stem cell transplantation, with melphalan as a preparative regimen, within 12 months of initiation of induction therapy for newly diagnosed myelomaXx_NEWLINE_xXRecipients of prior allogeneic hematopoietic stem cell transplantation for AML or acute leukemia of ambiguous lineage are eligible if they do not have graft-versus-host disease (GVHD) or they have quiescent GVHD whether or not they are receiving immunosuppressive therapyXx_NEWLINE_xXPatients 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 recoveryXx_NEWLINE_xXPrevious allogenic stem cell transplantation.Xx_NEWLINE_xXHematopoietic cell transplantation (HCT) recipientsXx_NEWLINE_xXPatients must be between 100 - 200 days after allogeneic stem cell transplantationXx_NEWLINE_xXPatients with relapsed or refractory disease following stem cell transplantation are permittedXx_NEWLINE_xXPatients who have undergone prior stem cell transplantation will not be excluded from study entry; at least 3 months must have elapsed since autologous or allogeneic stem cell transplantation; patients must have no evidence of active graft versus host diseaseXx_NEWLINE_xXPatients previously treated with allogeneic bone marrow or stem cell transplantation are ineligibleXx_NEWLINE_xXPatients who are immediate candidates for allogeneic bone marrow or stem cell transplantation; patients who refuse this option remain eligible and need to be documented as such in patient medical recordXx_NEWLINE_xXPatients who are eligible for autologous transplantationXx_NEWLINE_xXPatients with histologically confirmed CD20 positive B-cell non-Hodgkin lymphoma (NHL) who are candidates for autologous stem cell transplantation (SCT)Xx_NEWLINE_xXParticipants 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 collectionXx_NEWLINE_xXPatient who has undergone allogeneic stem cell transplantationXx_NEWLINE_xXDay > 100 after allogeneic hematopoietic stem cell transplantationXx_NEWLINE_xXPhase 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 allowedXx_NEWLINE_xXPatients 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 transplantXx_NEWLINE_xXPatients achieving < partial response following preceding chemotherapy (cohort 1) or < very good partial response following autologous stem cell transplantation (cohort 2)Xx_NEWLINE_xXPatients who have undergone prior allogeneic hematopoietic stem cell transplantationXx_NEWLINE_xXPatients who have undergone an allogeneic hematopoietic cell transplantation (HSCT) within the last 5 years (yrs) are eligible for enrollment if they have no signs or symptoms of active graft versus host disease (GvHD) and are off all immune suppressive medicationsXx_NEWLINE_xXSubjects must be relapsed/refractory. Prior stem cell transplantation is allowed.Xx_NEWLINE_xXAble to collect >= 1.5 x 10^6 CD34+/kg cell for transplantationXx_NEWLINE_xXHistory of allogeneic stem cell transplantationXx_NEWLINE_xXPatients that underwent allogeneic transplantation as a treatment of graft failureXx_NEWLINE_xXEligibility for potentially-curative therapy including hematopoietic stem-cell transplantationXx_NEWLINE_xXProgressive disease within 8 weeks of prior therapy or within 12 weeks after prior autologous stem cell transplantationXx_NEWLINE_xXGreater than approximately 6 months since autologous stem cell transplantationXx_NEWLINE_xXNo prior autologous or allogeneic hematopoietic cell transplantationXx_NEWLINE_xXEvidence of chronic or acute graft versus host disease or on-going treatment for graft versus host disease from prior allogeneic stem cell transplantationXx_NEWLINE_xXEvidence of relapse or progression of disease after transplantationXx_NEWLINE_xXPatients with prior autologous and allogeneic hematopoietic stem cell transplantation are eligible if patients are off immunosuppression for > 1 month and have no evidence of active graft versus host disease (GVHD) except grade 1 skin GVHDXx_NEWLINE_xXSubjects with histologically confirmed relapsed or treatment refractory AML with the exception of subjects who are in first relapse following a remission >12 months in duration and are eligible for standard therapies (e.g., chemotherapy or stem cell transplantation).Xx_NEWLINE_xXSubjects 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);Xx_NEWLINE_xXAny evidence of ongoing graft-versus-host disease (GVHD) in subjects with prior progenitor cell transplantation;Xx_NEWLINE_xXPatients that underwent allogeneic transplantation as a treatment of graft failureXx_NEWLINE_xXPatients who have undergone autologous/allogeneic stem cell transplantation are eligibleXx_NEWLINE_xXPrevious hematopoetic stem cell transplantation.Xx_NEWLINE_xXRecipient of an hematopoietic stem cell transplantation (HSCT)Xx_NEWLINE_xXPatients with neutropenic fever who have existing malignancy or have undergone hematopoietic stem cell transplantationXx_NEWLINE_xXPatients must meet institutional criteria for eligibility for non-myeloablative allogeneic stem cell transplantationXx_NEWLINE_xXThere are no liver function test criteria for non-myeloablative allogeneic stem cell transplantationXx_NEWLINE_xXPatients who are candidates for autologous stem-cell transplantation due to primary refractory or first relapse of diseaseXx_NEWLINE_xXPatients with adequate autologous stem cell collection for transplantation (target >= 2.5 x 10^6 CD34+ cells/kg)Xx_NEWLINE_xXSubjects with hematologic malignancies for whom allogeneic stem cell transplantation is deemed clinically appropriate.Xx_NEWLINE_xXAt the time of registration, stem cell transplantation is not planned within the next 3 monthsXx_NEWLINE_xXPatients 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 progressionXx_NEWLINE_xXPrior allogeneic hematopoietic stem cell transplantation (allogeneic stem cell transplant)Xx_NEWLINE_xXPrevious allogeneic stem-cell transplantationXx_NEWLINE_xXLess than 1 month since completion of autologous stem cell transplantation or less than 3 months since completion of allogeneic stem cell transplantationXx_NEWLINE_xXPrior history allogeneic stem cell transplantationXx_NEWLINE_xXMust be eligible for autologous transplantation according to institutional guidelinesXx_NEWLINE_xXPrior allogeneic bone marrow or peripheral blood stem cell transplantationXx_NEWLINE_xXPatients following allogeneic stem cell transplantation are eligible in the absence of graft versus host disease and are off immunosuppression for at least 30 daysXx_NEWLINE_xXPrior allogeneic stem cell transplantation (SCT), or autologous SCT within 100 days prior to Day 1 of Cycle 1Xx_NEWLINE_xXHistory of allogeneic stem cell transplantationXx_NEWLINE_xX“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 characteristicsXx_NEWLINE_xXHistory of allogeneic stem cell transplantationXx_NEWLINE_xXPrior allogeneic stem cell transplantationXx_NEWLINE_xXAllogeneic stem cell transplantation within the last 28 days before first treatment with graft versus host disease requiring more than 20 mg of steroids per day. Steroid dosage must be stable within two weeks prior to start of treatment.Xx_NEWLINE_xXPatients who are candidates for allogeneic stem cell transplantation (for patients with refractory or relapsed acute myeloid leukemia).Xx_NEWLINE_xXPrior autologous or allogeneic stem cell transplantationXx_NEWLINE_xXDiagnosis of AML or ALL, relapsed or refractory after at least 1 prior treatment regimen. Newly-diagnosed patients ? 60 years old who have refused or are considered unfit for standard chemotherapy regimens or stem cell transplantation are also eligible.Xx_NEWLINE_xXSubject needs heart transplantation.Xx_NEWLINE_xXHistory of previous bone marrow and/or stem cell transplantation.Xx_NEWLINE_xXNot eligible for an allogeneic hematopoietic stem cell transplantationXx_NEWLINE_xXPrior bone marrow/hematopoietic stem cell transplantationXx_NEWLINE_xXAt least 60 days must have elapsed from hematopoietic stem cell transplantation (HSCT)Xx_NEWLINE_xXEligible for autologous transplantationXx_NEWLINE_xXAllogeneic hematopoietic stem cell transplantation (HSCT) within 12 weeks before blinatumomab treatmentXx_NEWLINE_xXEligible for autologous stem cell transplantationXx_NEWLINE_xXPrior therapy with severely myelotoxic regimens, including autologous and allogenic stem cell transplantationXx_NEWLINE_xXAML relapse > 6 months since autologous or allogeneic stem cell transplantation, provided they are in first or second relapse and: No active graft-versus-host disease (GVHD > grade 1). No treatment with high dose steroids for GVHD (up to 20 mg Prednisolone or equivalent, Appendix G). No treatment with immunosuppressive drugs with the exception of low dose cyclosporine and tacrolimus (blood levels of 0.5-0.6 µg/mL).Xx_NEWLINE_xXHistologically confirmed (Myelodysplastic Syndromes) MDS or Acute Myeloid Leukemia (AML) undergoing allogeneic hematopoietic stem cell transplantation (HSCT) with either peripheral blood or bone marrow as the source of hematopoietic stem cells At the time of allogeneic HSCT:Xx_NEWLINE_xXRelapse after allogeneic stem cell transplantation prior to post-transplant day 30Xx_NEWLINE_xXPatients with prior autologous or allogeneic hematopoietic cell transplantation (HCT) are eligible if relapse occurs provided symptoms of graft-versus host disease are well controlled with stable use of immunosuppressive agentsXx_NEWLINE_xXNot a candidate for allogeneic stem cell transplantationXx_NEWLINE_xXPatients who have received allogeneic stem cell transplantation < 12 months prior to entering the studyXx_NEWLINE_xXPatients who have had prior allogeneic stem cell transplantation and show evidence of active graft-versus-host disease that requires immunosuppressive therapyXx_NEWLINE_xXImmunocompromised, 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 malignanciesXx_NEWLINE_xXPatients who have undergone T-cell depleted allogeneic hematopoietic stem cell transplantation at Memorial Sloan-Kettering Cancer Center (MSKCC) for:Xx_NEWLINE_xXPatients with active graft versus host disease after allogeneic stem cell transplantation. At least 3 months must have elapsed since completion of allogeneic stem cell transplantation except for patients with AML, where at least 2 months must have elapsed;Xx_NEWLINE_xXAllogeneic stem cell transplantationXx_NEWLINE_xXPrevious autologous or allogeneic stem cell transplantation.Xx_NEWLINE_xXAt 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).Xx_NEWLINE_xXPatients 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 permittedXx_NEWLINE_xXPatients who are candidates for high dose chemotherapy and autologous stem cell transplantation with curative intent should not be enrolledXx_NEWLINE_xXPrior autologous or allogeneic SCTXx_NEWLINE_xXHistory of previous bone marrow and/or stem cell transplantation.Xx_NEWLINE_xXPrior allogeneic stem cell transplantation.Xx_NEWLINE_xXPrevious allogeneic stem cell transplantation at any time OR autologous stem cell transplantation within 6 months of study entry.Xx_NEWLINE_xXPrior hematopoietic stem cell or bone marrow transplantationXx_NEWLINE_xXPrevious autologous stem cell transplantation within 6 months prior to randomization.Xx_NEWLINE_xXPrevious allogeneic stem cell transplantation.Xx_NEWLINE_xXThe patient has received, or is receiving, allogeneic Stem Cell Transplantation (SCT).Xx_NEWLINE_xXPrevious allogenic stem cell or allogeneic bone marrow transplantationXx_NEWLINE_xXThe patient has received, or is receiving induction chemotherapy followed by Stem Cell Transplantation.Xx_NEWLINE_xXThe patient declines to undergo stem cell transplantation orXx_NEWLINE_xXStem cell transplantation is not available to the patient due to cost or other reasonsXx_NEWLINE_xXAt 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 transplantationXx_NEWLINE_xXPrior allogeneic marrow or stem cell transplantationXx_NEWLINE_xXPrior autologous stem cell transplantation < 1 month or allogenic stem cell transplantation < 3 months prior to C1D1.Xx_NEWLINE_xXActive graft versus host disease (after allogeneic stem cell transplantation) at C1D1.Xx_NEWLINE_xXHistory of allogeneic bone marrow or stem cell transplantationXx_NEWLINE_xXPrior allogeneic hematopoietic stem-cell transplantation if evidence of donor chimerism persists; patients with exclusively autologous hematopoiesis are eligibleXx_NEWLINE_xXMeet standard criteria as defined by the institution for a myeloablative allogeneic stem cell transplantation, with myeloablative defined as using conditioning regimens containing:\r\n* Total-body irradiation (TBI) >= 1200 cGy, or \r\n* Busulfan >= 12.8 mg/kgXx_NEWLINE_xXSubject is not a candidate to undergo allogenic hematopoietic stem cell transplantation (HSCT).Xx_NEWLINE_xXPatients who will undergo their first autologous hematopoietic stem cell transplantation (HSCT) procedure as treatment for multiple myelomaXx_NEWLINE_xXAdults undergoing hematopoietic stem cell transplantation (HSCT) at the University of Wisconsin Carbone Cancer Center (UWCCC)Xx_NEWLINE_xXAll patients must have a histologic or cytological diagnosis of ALL treated with stem cell transplantation; there are no restrictions on prior therapyXx_NEWLINE_xXAny patient undergoing allogeneic hematopoietic stem cell transplantation (either 1st or subsequent)Xx_NEWLINE_xXScheduled to receive conditioning chemotherapy followed by upfront or salvage autologous peripheral blood hematopoietic stem cell transplantationXx_NEWLINE_xXPatients who have undergone a prior allogeneic or autologous stem cell transplantation within the previous six monthsXx_NEWLINE_xXPatient has CMV specific T-cells from the donor of his/her hematopoietic stem cell transplantation (HSCT) availableXx_NEWLINE_xXReceived a donor lymphocyte infusion (DLI) or hematopoietic cell transplantation (HCT) within 3 months of enrollmentXx_NEWLINE_xXPatients designated to undergo myeloablative or intermediate intensity allogeneic peripheral blood or bone marrow hematopoietic cell transplantation; consent will be obtained prior to admission for HSCT; patients receiving any donor source of stem cells are eligible; eligible conditioning regimens are those defined as myeloablative by the American Society of Blood and Marrow Transplantation (ASBMT) consensus criteria as well as the combination of fludarabine with melphalan (100-140 mg/mg^2)Xx_NEWLINE_xXPrior allogeneic hematopoietic stem cell transplantation; (patients may have received a prior autologous hematopoietic stem cell transplant)Xx_NEWLINE_xXUndergoing hematopoietic stem cell transplantation (HSCT) at the University of Wisconsin Carbone Cancer Center (UWCCC)Xx_NEWLINE_xXPatients who have undergone prior allogeneic transplantation are eligible provided that their transplant day 0 is > 6 months from their first dose of study drugXx_NEWLINE_xXNot eligible for stem cell transplantationXx_NEWLINE_xXRecipients of allogeneic hematopoietic cell transplantation (HCT) after either myeloablative or reduced intensity conditioning regimens; any donor source of stem cells is eligibleXx_NEWLINE_xXStem cell transplantation within preceding 60 days prior to registrationXx_NEWLINE_xXRecipients of allogeneic hematopoietic cell transplantation (HCT) after either myeloablative or reduced intensity conditioning regimens; any donor source of stem cells is eligibleXx_NEWLINE_xXTransplantation of PBSCXx_NEWLINE_xXPrevious allogeneic hematopoietic stem cell transplantationXx_NEWLINE_xXSubject underwent allogeneic stem cell transplantation at least 6 months prior to enrollmentXx_NEWLINE_xXPatients 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 regimenXx_NEWLINE_xXLess than 3 months from myeloablative conditioning for autologous transplantationXx_NEWLINE_xXPatients must have a hematologic malignancy for which allogeneic hematopoietic peripheral blood cell transplantation is deemed clinically appropriate. Eligible diseases and stages include the following:Xx_NEWLINE_xXPrior autologous or allogeneic HCT;Xx_NEWLINE_xXPatients who have undergone either ablative or non-myeloablative allogeneic stem cell transplantation are eligibleXx_NEWLINE_xXAllogeneic stem cell transplantation using a single or multiple umbilical cord blood units or using bone marrowXx_NEWLINE_xXAllogeneic 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)Xx_NEWLINE_xXPatients who in the opinion of the treating physician are unlikely to comply with the restrictions of allogeneic stem cell transplantation based on formal psychosocial screening; (i.e., serious, uncontrolled psychiatric illness/social situations that would limit compliance with study requirements)Xx_NEWLINE_xXOne or more prior allogeneic stem cell transplantation (prior autologous transplant is acceptable)Xx_NEWLINE_xXPrior allogeneic hematopoietic cell transplantation (HCT)Xx_NEWLINE_xXSubjects undergoing matched related full intensity allogeneic hematopoietic stem cell transplantation (HSCT)Xx_NEWLINE_xXPrior myeloablative allogeneic or autologous HSCTXx_NEWLINE_xXPatients must otherwise fulfill institutional criteria for eligibility to undergo myeloablative allogeneic stem cell transplantationXx_NEWLINE_xXPatients who have undergone allogeneic stem cell transplantation for the treatment of any hematological malignancy are eligibleXx_NEWLINE_xXHematologic disorder requiring allogeneic hematopoietic cell transplantationXx_NEWLINE_xXTransplantation with PBSCXx_NEWLINE_xXPrior allogeneic hematopoietic stem cell transplantationXx_NEWLINE_xXSubjects with hematologic malignancies or recipients of a first allogeneic or autologous hematopoietic stem cell transplantation and presently clinically stableXx_NEWLINE_xXLess than 3 months from myeloablative conditioning for autologous transplantation (if applicable)Xx_NEWLINE_xXPatients who have had stem-cell transplantationXx_NEWLINE_xXPrior stem cell transplantationXx_NEWLINE_xXEligible for haploidentical stem cell transplantation according to the investigatorXx_NEWLINE_xXAutologous stem cell transplantation less than 90 days prior to study day 1Xx_NEWLINE_xXHematopoietic stem cell transplantation (HSCT) within 60 days of screening, or receipt of immunosuppressive therapy for graft-versus-host disease treatment or prophylaxis within 14 days of first protocol therapy, or active graft-versus-host-diseaseXx_NEWLINE_xXPrior autologous stem cell transplantation < 1 month or allogeneic stem cell transplantation < 4 months prior to C1D1.Xx_NEWLINE_xXActive graft versus host disease (after allogeneic stem cell transplantation) at C1D1.Xx_NEWLINE_xXHas received hematopoietic stem cell transplantation (HSCT) within 60 days of the first dose of DS-3201bXx_NEWLINE_xXPatients must not have had prior stem cell transplantation (autologous or allogeneic)Xx_NEWLINE_xXPatients with history of allogeneic stem cell transplantationXx_NEWLINE_xXPatients who have undergone prior allogeneic transplantation are eligible provided they do not have significant active graft versus host disease and that their transplant day 0 is > 6 months from their first dose of chemotherapyXx_NEWLINE_xXPatients receiving autologous stem cell transplantation must wait 8 weeks before initiation of study drug administration.Xx_NEWLINE_xXPatients who have previously undergone hematopoietic stem cell transplantation (SCT) or who are scheduled for SCTXx_NEWLINE_xXPrior autologous or allogeneic stem cell transplantation (SCT) within 12 weeks of initiation of study treatmentXx_NEWLINE_xXPrior allogeneic hematopoietic cell transplantation (HCT) with active graft versus host disease (GVHD) on therapeutic dosing of immunosuppression or prednisone > 20 mg daily equivalentXx_NEWLINE_xXHistory of allogeneic stem cell transplantationXx_NEWLINE_xXNot a candidate for or refusing treatment with hematopoietic stem cell transplantationXx_NEWLINE_xXPatients with a history of allogeneic hematopoietic stem cell transplantation (HSCT) will be eligible if they are more than 90 days removed from the date of stem cell infusion, have no evidence of acute graft-versus-host disease (GVHD) or active chronic (grade 2-4) GVHD, and are off of all transplant-related immunosuppression for at least 2 weeksXx_NEWLINE_xXPrior intensive chemotherapy or stem cell transplantation for the treatment of myelodysplastic syndromeXx_NEWLINE_xXNot a candidate for, or refusing treatment with hematopoietic stem cell transplantationXx_NEWLINE_xXHas undergone prior allogeneic hematopoietic stem cell transplantation within the last 5 years. Note: Participants who have had a transplant greater than 5 years ago are eligible as long as there are no symptoms of graft-versus-host disease (GVHD).Xx_NEWLINE_xX