Inclusion Criteria:

          -  Pathologically (histologically or cytologically) proven diagnosis of recurrent or
             persistent ovarian endometrioid or clear cell carcinoma, OR recurrent or persistent
             endometrioid endometrial adenocarcinoma; patients with recurrent endometrial cancer
             must have mismatch repair (MMR) immunohistochemistry completed; if they are found to
             be mismatch repair deficient, they should be offered treatment with immune checkpoint
             inhibition before consideration for treatment on trial; primary ovarian tumors must be
             at least 50% endometrioid or clear cell morphology, or have histologically documented
             recurrence with at least 50% endometrioid or clear cell morphology; institutional
             pathology reports must be provided indicating at least 50% endometrioid or clear cell
             morphology for ovarian tumors (primary or recurrent lesions)

          -  All patients must have measurable disease as defined by Response Evaluation Criteria
             in Solid Tumors (RECIST) version (v) 1.1; measurable disease is defined as at least
             one lesion that can be accurately measured in at least one dimension (longest diameter
             to be recorded); each lesion must be >= 10 mm when measured by computed tomography
             (CT), magnetic resonance imaging (MRI) or caliper measurement by clinical exam; or >=
             20 mm when measured by chest x-ray; lymph nodes must be > 15 mm in short axis when
             measured by CT or MRI

          -  Patients must have had at least one, but no more than 3, prior cytotoxic regimens for
             management of primary disease; unlimited prior hormonal therapy, targeted therapy
             (including immunotherapy) or antiangiogenic therapy will be permitted

          -  Patients must have completed prior therapy:

               -  Chemotherapy: cytotoxic

                    -  At least 28 days since last dose of chemotherapy prior to registration.

               -  Chemotherapy: nitrosoureas

                    -  At least 6 weeks since last dose of chemotherapy prior to registration.

               -  Chemotherapy: non-cytotoxic (e.g. small molecule inhibitor)

                    -  At least 28 days since last dose of chemotherapy prior to registration.

               -  Monoclonal antibody(ies)

                    -  At least 28 days since last dose of monoclonal antibody prior to
                       registration.

               -  Immunotherapy

                    -  At least 28 days since last dose of immunotherapy prior to registration.

               -  Radiotherapy (RT)

                    -  At least 14 days from last local site RT prior to registration.

                    -  At least 21 days from stereotactic radiosurgery prior to registration.

                    -  At least 12 weeks from craniospinal, >= 50% radiation of pelvis or total
                       body irradiation prior to registration.

                    -  Patients with central nervous system (CNS) disease should demonstrate
                       evidence of stabilization after the 28-day time point after definitive
                       treatment.

                    -  Full recovery of radiation related side effects prior to registration.

                    -  All subjects must have evidence of measurable disease outside of the
                       radiation field at the time of registration.

          -  Appropriate stage for study entry based on the following diagnostic workup:

               -  History/physical examination within 14 days prior to registration

               -  Imaging of the chest, abdomen and pelvis within 28 days prior to registration

          -  Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1 or 2 within 14
             days prior to registration

          -  Platelets >= 100,000/mcl (within 14 days prior to registration)

          -  Absolute neutrophil count (ANC) >= 1,500/mcl (within 14 days prior to registration)

          -  Hemoglobin (Hgb) >= 8 g/dL (within 14 days prior to registration)

          -  Differential with no clinically significant morphologic abnormalities on complete
             blood count (CBC) testing; manual differential is encouraged, if clinically indicated,
             and in cases where an automated differential is abnormal (within 14 days prior to
             registration)

          -  Creatinine =< 1.5 x institutional/laboratory upper limit of normal (ULN) (within 14
             days prior to registration)

          -  Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =< 3 x ULN (within
             14 days prior to registration)

          -  Total serum bilirubin level =< 1.5 x ULN; direct bilirubin =< ULN for subjects with
             total bilirubin > 1.5 x ULN (patients with isolated indirect bilirubin elevations and
             a history of Gilbert's syndrome are eligible) (within 14 days prior to registration)

          -  Women of childbearing potential must be willing and able to use adequate contraception
             (hormonal and barrier method of birth control; abstinence) prior to study entry, for
             the duration of study participation, and for 30 days after the last dose of study
             agent; should a woman become pregnant or suspect she is pregnant while she is
             participating in this study, she should inform her treating physician immediately;
             theoretically, CYP3A induction with tazemetostat use may result in the loss of
             efficacy in hormonal contraceptives, thus a barrier method of contraception must be
             used in addition to hormonal contraceptives due to the potential drug-drug interaction
             with tazemetostat

          -  The patient or a legally authorized representative must provide study-specific
             informed consent and authorization permitting release of personal health information
             prior to study entry

          -  Patients with a prior or concurrent malignancy whose natural history or treatment does
             not have the potential to interfere with the safety or efficacy assessment of the
             investigational regimen are eligible for this trial

        Exclusion Criteria:

          -  Prior treatment with an investigational EZH2 inhibitor

          -  Patients who are unable to swallow pills or absorb orally administered medication

          -  A prior history of myeloid malignancies, including myelodysplastic syndrome (MDS)

          -  Abnormalities known to be associated with MDS (e.g. del 5q, chr 7 abn) and
             myeloproliferative neoplasms (MPN) (e.g. JAK2 V617F) observed in cytogenetic testing
             and deoxyribonucleic acid (DNA) sequencing

          -  A prior history of T-cell lymphoblastic lymphoma (T-LBL)/T-cell acute lymphoblastic
             leukemia (T-ALL)

          -  Severe, active co-morbidity per the treating investigator's discretion

          -  Pregnant or lactating patients

          -  Known human immunodeficiency virus (HIV) positive patients on combination
             antiretroviral therapy are ineligible because of the potential for pharmacokinetic
             interactions with tazemetostat; in addition, treatments involved in this protocol may
             be immunosuppressive, increasing the risk of lethal infections in this patient
             population

          -  Treatment with strong inhibitors or inducers of CYP3A within 14 days of registration
             and during the study treatment