Patients must not be candidates for allogeneic hematopoietic stem cell transplant; NOTE: Subjects up to age 70 years who are considered fit for allogeneic hematopoietic stem cell transplant, should be considered for enrollment on E1910, in order to avoid competing with that study; if a patient is considered unfit for intensive chemotherapy at the time of initial diagnosis, but subsequently achieves a complete remission (CR), then it will be left to the treating physician’s discretion to consider hematopoietic stem cell transplant (HSCT) ELIGIBILITY CRITERIA - PHASE II (ARM D): Patient may be enrolled with a prior allogeneic hematopoietic stem cell transplant (HSCT) but the transplant date must be at least 90 days before date of enrollment; patient must be off immunosuppression and without active GVHD prior to enrollment if previous HSCT Gene therapy using an integrating vector Allogeneic hematopoietic stem cell transplant at any time not permitted Prior allogeneic hematopoietic cell transplant Subjects with prior autologous and allogeneic hematopoietic stem cell transplantation (allo HSCT) are eligible. Intention to proceed to high dose chemotherapy (HDT) and autologous hematopoietic stem cell transplant (HSCT) Adult male and female subjects at least 18 years of age who have had allogenic bone marrow transplant (BMT) or hematopoietic stem cell transplantation (HSCT). Prior allogeneic hematopoietic stem cell transplantation (allo HSCT) Prior allogeneic hematopoietic cell transplant Previous allogeneic hematopoietic stem cell transplant Allogeneic hematopoietic stem cell transplant Prior allogeneic transplant for any hematopoietic disorder Subject is a candidate for hematopoietic stem cell transplantation (HSCT). Prior cell or gene therapy, excluding transfers of genetically unmodified autologous cells (eg. Hematopoietic stem cell transplantation), at any time; or prior allogeneic HSCT at any time DONOR: Testing for communicable disease will be performed according to the University of Washington (UW) Hematopoietic Stem Cell Transplant Program guidelines set forth in the most current standard operating policies and procedures (UW Foundation for the Accreditation of Cellular Therapy [FACT]-accredited Clinical Hematopoietic Cell Processing Laboratory [CHCPL] standard of procedure [SOP]) for hematopoietic cell donor evaluation and selection Immunosuppression following a Hematopoietic Stem Cell Transplantation (HSCT) within 6 weeks prior to study entry; Allogeneic hematopoietic stem cell transplantation (HSCT) within 24 weeks before the start of protocol-specified therapy. Either not eligible or unwilling to proceed with hematopoietic stem cell transplantation (HSCT) Eligible for, have a suitable donor, and are willing to undergo hematopoietic stem cell transplantation (HSCT) Previous allogeneic hematopoietic cell transplant (HCT) History of hematopoietic stem cell transplant (HSCT) Has previously received an allogeneic hematopoietic cell transplant or chimeric antigen receptor-modified (CAR)-T cells Diagnosis of AML and MDS according to World Health Organization (WHO) classification that underwent first allogeneic hematopoietic cell transplant (HSCT) with either peripheral blood or bone marrow as the source of the hematopoietic stem cells Prior allogeneic hematopoietic cell transplant. Has received allogeneic hematopoietic stem cell transplant within 3 months of CAR T cell infusion; hematopoietic stem cell transplant (HSCT) > 3 months from CAR T cell infusion eligible Individuals who are eligible for allogeneic hematopoietic stem cell transplantation (HSCT) as determined by the treating physician, and have a suitable donor or appropriate stem cell source available Study enrollment no earlier than 3 months after preceding hematopoietic cell transplantation (HSCT) Patients who have received a prior allogeneic hematopoietic stem cell transplant (HSCT) and who have either rejected their grafts or who have become tolerant of their grafts with no active GVHD requiring immunosuppressive therapy Prior autologous or allogeneic hematopoietic stem cell Preceding allogeneic hematopoietic stem cell transplant (HSCT) - Participant is not a candidate to undergo intensive chemotherapy or allogeneic hematopoietic stem cell transplantation (HSCT). Malignant conditions or other life threatening disorders correctable by transplant for which CD34+ selected, T-cell depleted allogeneic hematopoietic stem cell transplantation is indicated such as: No subjects who have received an allogeneic hematopoietic stem cell transplant are eligible Received an allogeneic hematopoietic transplant within 3 months of screening Have active malignancy with the exception of nonmelanoma skin cancer. Subjects who have had a hematopoietic stem cell transplant (HSCT) and who experience relapse or progression of the malignancy as per investigator's opinion are not to be enrolled. Evidence of multiple myeloma disease progression (as defined by IMWG) any time prior to autologous (auto)-hematopoietic stem cell transplant (HSCT) Prior autologous or allogeneic hematopoietic stem cell transplantation (HSCT) Prior allogeneic transplant for any hematopoietic disorder Subject is refractory to or relapsed after first-line AML therapy (with or without hematopoietic stem cell transplant (HSCT)). Hematopoietic cell transplantation (At least 60 days from infusion of hematopoietic cells prior to first dose of tazemetostat) Prior allogeneic hematopoietic stem cell transplant. Subject who has history of organ transplant or allogeneic hematopoietic stem cell transplantation. Subjects with relapsed primary disease, or subjects who have been treated for relapse after the allogeneic hematopoietic stem-cell transplantation (allo-HSCT) was performed. Prior allogeneic hematopoietic stem cell transplant (HSCT) with either standard or reduced intensity conditioning ? 6 months. Patients who have previously undergone allogeneic hematopoietic stem cell transplant will be excluded from this study The patient has received any hematopoietic stem cell transplantation (HSCT) ? 3 months prior to start of Investigational Product. Allogeneic hematopoietic stem cell transplant within 100 days prior to leukapheresis Prior history of allogeneic hematopoietic stem cell transplant (HSCT). Recipients of prior allogeneic hematopoietic stem cell transplant (HSCT) with active acute or chronic GVHD Prior allogeneic hematopoietic stem cell transplant Prior allogeneic hematopoietic stem cell transplant Hematopoietic stem cell transplant (HSCT) patients with symptomatic hemorrhagic cystitis (minimal grade 1 symptoms of HC per NCI criteria) and positive BKV in urine > 1 x 10^3 deoxyribonucleic acid (DNA) copies/ml Recipient of an hematopoietic stem cell transplantation (HSCT) Prior autologous or allogeneic hematopoietic stem cell transplant (HSCT) Prior allogeneic hematopoietic stem cell transplant. Prior allogeneic hematopoietic stem cell transplant (HSCT) Prior allogeneic hematopoietic stem cell transplant Patient must not be a candidate for an allo-hematopoietic stem cell transplant (HSCT) At least 100 days after receiving any allogeneic hematopoietic stem cell transplant AND Previous allogeneic hematopoietic stem cell transplant (HSCT transplant). Allogeneic hematopoietic stem cell transplant or Donor Lymphocyte Infusion within 90 days prior to to the first dose of study drug Prior allogeneic hematopoietic stem cell transplant Prior allogeneic hematopoietic stem cell transplant within