Testing the Addition of the Anti-cancer Drug, Tazemetostat, to the Usual Treatment (Dabrafenib and Trametinib) for Metastatic Melanoma That Has Progressed on the Usual Treatment

Inclusion Criteria: * Patient must have a diagnosis of BRAF\^V600E/K-mutated metastatic melanoma * Patient must have had documented radiographic or clinical evidence of progressive disease while on combination BRAF/MEK inhibitor therapy. For Phase 2 only, no more than one intervening therapy since progression on BRAF/MEK inhibitor therapy is allowed. Subjects who have evidence of progression while on, or within 4 weeks of completing, combination BRAF/MEK inhibitor therapy in the adjuvant setting will be eligible * PHASE 2 ONLY: Patient must have EZH2 alteration (somatic mutation or copy number alteration). Can be performed on either archival or fresh specimen. EZH2 alterations need to be documented by a Clinical Laboratory Improvement Act (CLIA)/Clinical Laboratory Improvement Program (CLIP)-certified next generation sequencing platform (Foundation One, Tempus, Guardant360, etc.) * PHASE 2 ONLY: Patient must have measurable disease * PHASE 2 ONLY: Patient must have at least one tumor lesion amenable to biopsy. If possible, this lesion should be different from the lesion used for following tumor measurements but is not required * PHASE 2 ONLY: Patient must agree to planned pre-treatment and planned on-treatment biopsy. A pre-treatment biopsy will be optional if patient has an archival tissue block or 5 formalin-fixed paraffin-embedded (FFPE) slides available from specimen used to document presence of eligible EZH2 alteration that is deemed adequate for evaluation * Patient mu…