Patient must not have received any prior marrow-ablative chemotherapy and autologous hematopoietic cell transplant Recipients of prior autologous hematopoietic stem cell transplantation are ineligible if disease recurrence occurred less than months from their autologous stem cell transplant. Intention to proceed to high dose chemotherapy (HDT) and autologous hematopoietic stem cell transplant (HSCT) relapse within year from frontline chemo-immunotherapy and ineligible for autologous hematopoietic stem cell transplant (auto-HSCT) relapse within year from frontline chemo-immunotherapy and ineligible for autologous hematopoietic stem cell transplant (auto-HSCT) Has received prior autologous hematopoietic stem cell transplant within the last days Non-Hodgkin's lymphoma (NHL) in second or third complete remission, or relapse (including relapse post autologous hematopoietic stem cell transplant); relapsed double hit lymphomas; patients with options for treatment that are known to be curative are not eligible Hodgkin's disease (HD): Induction failures, after first complete remission, or relapse (including relapse post autologous hematopoietic stem cell transplant), or those with active disease Mantle cell lymphoma patients who are beyond first remission and previously treated with chemoimmunotherapy; patients who have relapsed following autologous hematopoietic cell transplant (HCT) are eligible High dose therapy with autologous hematopoietic cell infusion (At least days from last infusion prior to first dose of tazemetostat) Prior autologous or allogeneic hematopoietic stem cell Patients must not have a prior autologous, syngeneic or allogeneic hematopoietic stem cell transplant History of relapsed or refractory CD+ malignancies (e.g. non Hodgkin lymphoma) who have failed prior treatment and require autologous hematopoietic stem cell transplant; evidence of disease not required (cohort ) Multiple myeloma (MM) stage II or III patients who have progressed after an initial response to chemotherapy or autologous hematopoietic stem cell transplantation (HSCT) or MM patients with refractory disease who may benefit from tandem autologous-nonmyeloablative allogeneic transplant Stem cells from an identical donor could be used for autologous hematopoietic cell transplant (HCT) Hodgkin's disease (HD): induction failures, second or third complete remission, or relapse (including relapse post autologous hematopoietic stem cell transplant) Evidence of multiple myeloma disease progression (as defined by IMWG) any time prior to autologous (auto)-hematopoietic stem cell transplant (HSCT) Prior allogeneic or autologous hematopoietic stem cell transplant in the last months Unless approved by the medical monitor, may not have received autologous hematopoietic stem cell transplant within months before treatment Autologous hematopoietic cell infusion after high dose therapy At least days Considered eligible for hematopoietic stem cell transplant (allogeneic or autologous) at the time of signing the ICF. Received autologous hematopoietic stem cell transplant within the last months Prior autologous hematopoietic stem cell transplant ? months. Research participant did not have evidence of disease progression after salvage therapy and therefore underwent an autologous myeloablative transplantation with hematopoietic progenitor cell autologous (HPC[A]) rescue procedure Non-Hodgkin's lymphoma - induction failures, second or third complete remission, or relapse (including relapse post autologous hematopoietic stem cell transplant) Hodgkin's disease - induction failure, second or later complete remission, or relapse (including relapse post autologous hematopoietic stem cell transplant) Hodgkin's disease (HD): induction failures, second or third complete remission, or relapse (including relapse post autologous hematopoietic stem cell transplant); or Prior autologous hematopoietic stem cell transplant Prior autologous or allogeneic hematopoietic stem cell transplant (HSCT) Prior autologous hematopoietic stem cell transplant within days of study entry Autologous hematopoietic stem cell transplant or fludarabine chemotherapy within months of study enrollment Prior autologous hematopoietic stem cell infusion < weeks prior to first study dose Prior autologous or allogeneic hematopoietic stem cell transplant Receiving a G-CSF for one of the following indications:\r\n* Prevention/treatment of neutropenia along with treatment for leukemia or lymphoma\r\n* Mobilization of hematopoietic progenitor cells\r\n* Neutropenia prevention following autologous hematopoietic cell transplant Scheduled to undergo either autologous or allogeneic hematopoietic stem cell transplant Prior autologous or allogeneic hematopoietic stem cell transplant Non-allogeneic (e.g. autologous) or syngeneic hematopoietic stem cell transplant (SCT) recipients Non-allogeneic (e.g. autologous) or syngeneic hematopoietic stem cell transplant (SCT) recipients Prior allogeneic or autologous hematopoietic stem cell transplant in past months Have documented or anticipated neutropenia expected to last for at least days, following treatment in at least one of the following clinical situations: acute leukemia, myelodysplasia, severe aplastic anemia, recipients of Autologous hematopoietic stem cell transplant (HSCT), high risk neuroblastoma, advanced stage non-Hodgkin's lymphoma, hemophagocytic lymphohistiocytosis Autologous hematopoietic stem cell transplant < months prior to enrollment.