Mass General - Division of Clinical Research

Participants must meet ALL the following inclusion criteria to be eligible to enroll in this study: 1. Have voluntarily agreed to provide written informed consent and demonstrated willingness and ability to comply with all aspects of the protocol. Study related activities will not start until written consent is obtained. 2. Life expectancy ≥ 3 months before enrollment 3. Phase 1b: 18-65 years old histologically confirmed Soft Tissue Sarcoma 4. Phase 3: ≥18 years old with unresectable locally advanced or metastatic Epithelioid Sarcoma and tumor tissue available 5. Have measurable disease 6. ECOG performance status of 0, 1, or 2 7. Have adequate hematologic (bone marrow [BM] and coagulation factors), renal and hepatic function as required per protocol 8. Females must not be lactating or pregnant at Screening or Baseline 9. Females must not be pregnant or breast feeding and agree to use highly effective contraception during the clinical trial and for 6 months following the final dose of study 10. Male participants of child-bearing potential must have had either a successful vasectomy or practice highly effective contraception 11. Participants diagnosed with human immunodeficiency virus (HIV) are eligible to participate in the study if their infection is well controlled on anti-retroviral therapy.

Participants meeting ANY of the following exclusion criteria are NOT eligible to enroll in this study: 1. Prior exposure to tazemetostat or other inhibitor(s) of enhancer of zeste homologue-2 (EZH2). 2. Prior systemic anticancer therapy. 3. Contraindications noted in the doxorubicin label 4. Have any prior history of myeloid malignancies, including myelodysplastic syndrome (MDS) or acute myeloid leukemia (AML). 5. Have prior history of T-cell lymphoblastic lymphoma/T-cell acute lymphoblastic leukemia (T- LBL/T-ALL). 6. Have participated in another interventional clinical study and received investigational drug within 30 days or 5 half-lives, whichever is longer, prior to the planned first dose of study treatment. 7. Have known active central nervous system (CNS) or any leptomeningeal metastasis of primary extracranial tumor. 8. Participants taking medications that are known potent cytochrome P450 (CYP)3A4 inducers/inhibitors (including St. John's Wort) 9. Are unwilling to exclude Seville oranges, grapefruit juice, AND grapefruit from the diet and all foods that contain those fruits from time of enrollment to through the duration of study participation. 10. Major surgery within 4 weeks before the first dose of study treatment. Participants must have recovered from surgery prior to enrollment to this study. 11. Are unable to take oral medication OR have malabsorption syndrome or any other uncontrolled gastrointestinal condition (eg, nausea, diarrhea, vomiting) that might impair the bioavailability of study treatment. 12. Have an active infection requiring systemic therapy. 13. Are immunocompromised (ie, has a congenital immunodeficiency). 14. Have known hypersensitivity to any component of tazemetostat or doxorubicin. 15. Cardiovascular impairment as stated in the protocol 16. Have a known active infection with hepatitis B virus (HBV, as measured by positive hepatitis B surface antigen), hepatitis C virus (HCV, as measured by positive hepatitis C antibody). 17. Any other major illness that, in the Investigator's judgment, will substantially increase the risk associated with the participant's participation in this study OR interfere with their ability to receive study treatment or complete the study. 18. Female participants who are pregnant or breastfeeding. 19. Participants who have undergone a solid organ transplant. 20. Participants with malignancies other than STS (phase 1b) or ES (Phase 3 only). 21. Participants housed in an institution by order of the authorities or courts.