Inclusion Criteria:

• Have voluntarily agreed to provide written informed consent and demonstrated willingness and ability to comply with all aspects of the protocol.
• Are aged 18 years at the time of providing voluntary written informed consent. informed consent. 18 years at the time of providing voluntary written informed consent.
• Life expectancy 3 months before enrollment. 3 months before enrollment.
• Phase 1b: Have histologically confirmed STS.
• Phase 3: Have histologically confirmed epithelioid sarcoma, with loss of INI1 or SMARCA4 confirmed by IHC, or molecular confirmation of tumor bi-allelic INI1 or SMARCA4 loss or mutation when INI1 or SMARCA4 IHC is equivocal or unavailable.
• Have measurable disease as defined by the Response Evaluation Criteria in Solid.
• ECOG performance status of 0, 1, or 2.
• Females must not be lactating or pregnant at Screening or Baseline.
• Females of childbearing potential must not have had unprotected sexual intercourse within 30 days prior to study entry and must agree to use a highly effective method of contraception, from the last menstrual period prior to randomization, during Treatment cycles, and for 6 months after the final dose of study treatment, and have a male partner who uses a condom.
• Male subjects must have had either a successful vasectomy OR they and their female partner must meet the criteria above (ie, not of childbearing potential OR practicing highly effective contraception and use a condom throughout the study period and for 6 months after doxorubicin discontinuation or 30 days after oral study treatment [tazemetostat or placebo] discontinuation, whichever is later).
• Additional Inclusion Criteria for subjects with diagnosed human immunodeficiency virus (HIV).

Exclusion Criteria:

• Prior exposure to tazemetostat or other inhibitor(s) of enhancer of zeste homologue-2 (EZH2).
• Prior systemic anticancer therapy.
• Subjects must not have any of the contraindications noted in the local doxorubicin label (i.e., Summary of Product Characteristics [SmPc] or United States Prescribing Information [USPI]).
• Have any prior history of myeloid malignancies, including myelodysplastic syndrome (MDS) or acute myeloid leukemia (AML).
• Have prior history of T-cell lymphoblastic lymphoma/T-cell acute lymphoblastic leukemia (T-LBL/T-ALL).
• 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.
• Have known active central nervous system (CNS) or any leptomeningeal metastasis of primary extracranial tumor. Subjects with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging 4 weeks prior to the first dose of study treatment and any neurologic symptoms have stabilized), have no evidence of new or enlarging brain metastases, and are on stable or tapering doses of steroids for at least 7 days prior to first dose of study treatment.
  • NOTE: Subjects with asymptomatic brain metastases found on screening magnetic resonance imaging (MRI) may be entered into the study without prior radiation therapy to the brain if they do not require immediate surgical or radiation therapy in the opinion of the treating Investigator and in the opinion of a radiation therapy or neurosurgical consultant.
• Subjects taking medications that are known potent cytochrome P450 (CYP)3A4 inducers/inhibitors (including St. John's Wort) 
• Additional Exclusion Criteria apply.