Eligible for Autologous Hematopoietic stem cell transplantation according at the investigator discretion. Previous hematopoietic stem cell transplantation; patients can have had prior relapsed disease as long as they have never been previously transplanted 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 Subjects with prior autologous and allogeneic hematopoietic stem cell transplantation (allo HSCT) are eligible. Has undergone prior allogeneic hematopoietic stem cell transplantation within the last years. Has ever received or is scheduled to receive an Allogeneic Hematopoietic Stem Cell Transplantation (alloHSCT) 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 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. Adult male and female subjects at least 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) Patients who have had an allogeneic hematopoietic stem cell transplantation are not eligible. Patient has an appropriate donor identified for 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 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 Subject is a candidate for hematopoietic stem cell transplantation (HSCT). Patients 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 cirrhosis 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 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. Immunosuppression following a Hematopoietic Stem Cell Transplantation (HSCT) within weeks prior to study entry; Allogeneic hematopoietic cell transplantation within years of study drug administration Allogeneic hematopoietic stem cell transplantation (HSCT) within weeks before the start of protocol-specified therapy. PHASE I: Patients who underwent an allogeneic hematopoietic stem cell transplantation from any donor source for acute lymphocytic leukemia PHASE II: Patients who underwent an allogeneic hematopoietic stem cell transplantation from any donor source for acute lymphocytic leukemia 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) Must have undergone allogeneic hematopoietic stem cell transplantation (HSCT) (regardless of stem cell source) History of prior autologous hematopoietic cell transplantation Prior hematopoietic transplantation is allowed (autologous and/or allogeneic) Has undergone prior allogeneic hematopoietic stem cell transplantation within the last years 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. Previous allogeneic hematopoietic stem cell transplantation Patients are planned for treatment with high dose melphalan and autologous hematopoietic cell transplantation (HCT) Prior history of allogeneic hematopoietic cell transplantation Prior hematopoietic transplantation is allowed (autologous and/or allogeneic) 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 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 months after preceding hematopoietic cell transplantation (HSCT) Prior high dose chemotherapy for autologous hematopoietic cell transplantation or prior allogeneic transplantation Prior allogeneic hematopoietic progenitor cell transplantation Prior autologous hematopoietic progenitor cell transplantation if the conditioning regimen included total body irradiation Patients with psychological or medical condition that patient's physician deems unacceptable to proceed to allogeneic hematopoietic stem cell transplantation 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 Malignant conditions for which CD+ selected, T-cell depleted allogeneic hematopoietic stem cell transplantation is indicated such as: - 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 CD+ selected, T-cell depleted allogeneic hematopoietic stem cell transplantation is indicated such as: Patients eligible for hematopoietic stem cell transplantation Prior allogeneic hematopoietic stem cell transplantation within previous days Prior allogeneic (allo)-hematopoietic cell transplantation (HCT) less than three months from the time of enrollment Patients who have received allogeneic hematopoietic stem cell transplantation are ineligible Prior allogeneic hematopoietic cell transplantation Prior high-dose chemotherapy and autologous hematopoietic cell transplantation (HCT)(s) is (are) allowed Prior autologous or allogeneic hematopoietic stem cell transplantation (HSCT) Hematopoietic cell transplantation (At least days from infusion of hematopoietic cells prior to first dose of tazemetostat) Allogeneic hematopoietic stem cell transplantation within the last years. Not a candidate for curative therapy or hematopoietic stem-cell transplantation (either due to disease burden, fitness, or preference). Patients who have undergone autologous hematopoietic stem cell transplantation are eligible once they have recovered from all toxicities from therapy Have had at least days between prior hematopoietic stem cell transplantation (SCT) and first dose of study drug. Hematopoietic stem cell transplantation ? months of dosing Has undergone prior allogeneic hematopoietic stem cell transplantation within the last years. (Subjects who have had a transplant greater than years ago are eligible as long as there are no symptoms of GVHD.) Patients must have undergone autologous hematopoietic stem cell transplantation (AHCT) and achieved engraftment by day (D)- as evidenced by absolute neutrophil count (ANC) > /mcL and platelets (Plt) > ,/mcL Has received more than 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. 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 months prior to start of conditioning Prior allogeneic hematopoietic stem cell transplantation Prior hematopoietic stem cell transplantation The patient has received any hematopoietic stem cell transplantation (HSCT) ? months prior to start of Investigational Product. Recipients of prior allogeneic hematopoietic stem cell transplantation Hematopoietic cell transplantation (HCT) recipients Day > after allogeneic hematopoietic stem cell transplantation Patients who have undergone prior allogeneic hematopoietic stem cell transplantation Eligibility for potentially-curative therapy including hematopoietic stem-cell transplantation No prior autologous or allogeneic hematopoietic cell transplantation Recipient of an hematopoietic stem cell transplantation (HSCT) Patients with neutropenic fever who have existing malignancy or have undergone hematopoietic stem cell transplantation Not eligible for an allogeneic hematopoietic stem cell transplantation At least days must have elapsed from hematopoietic stem cell transplantation (HSCT) Allogeneic hematopoietic stem cell transplantation (HSCT) within weeks before blinatumomab treatment Histologically 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: 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 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 Adults undergoing hematopoietic stem cell transplantation (HSCT) at the University of Wisconsin Carbone Cancer Center (UWCCC) Any patient undergoing allogeneic hematopoietic stem cell transplantation (either st or subsequent) Scheduled to receive conditioning chemotherapy followed by upfront or salvage autologous peripheral blood hematopoietic stem cell transplantation Patient has CMV specific T-cells from the donor of his/her hematopoietic stem cell transplantation (HSCT) available Prior allogeneic hematopoietic stem cell transplantation; (patients may have received a prior autologous hematopoietic stem cell transplant) Undergoing hematopoietic stem cell transplantation (HSCT) at the University of Wisconsin Carbone Cancer Center (UWCCC) Previous allogeneic hematopoietic stem cell 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) Subjects undergoing matched related full intensity allogeneic hematopoietic stem cell transplantation (HSCT) Hematologic disorder requiring allogeneic hematopoietic cell transplantation Prior allogeneic hematopoietic stem cell transplantation Subjects with hematologic malignancies or recipients of a first allogeneic or autologous hematopoietic stem cell transplantation and presently clinically stable Has received hematopoietic stem cell transplantation (HSCT) within days of the first dose of DS-b Not a candidate for or refusing treatment with hematopoietic stem cell transplantation Not a candidate for, or refusing treatment with hematopoietic stem cell transplantation