Inclusion Criteria:

          -  Diagnosis:

               -  Phase 1 specific: recurrent or metastatic head and neck cancer, inclusive of
                  cancers that originate in the head and neck, except central nervous system (CNS)
                  cancers.

               -  Phase 2 specific: recurrent or metastatic head and neck squamous cell carcinoma
                  of the oral cavity, oropharynx, larynx or hypopharynx.

          -  Disease Evaluation:

               -  Phase 1 specific: Measurable or evaluable disease

               -  Phase 2 specific: Measurable disease per RECIST. Measurable disease defined as
                  lesions that can be accurately measured in at least one dimension (longest
                  diameter to be recorded) as ≥ 10 mm with CT scan, as ≥ 20 mm by chest x-ray, or ≥
                  10 mm with calipers by clinical exam.

          -  Phase 2 specific: Progression of disease, as assessed by RECIST, that occurred on
             prior pembrolizumab or nivolumab (given alone or with other therapy) in the last 6
             months.

          -  Phase 2 specific: PD-L1 positive (CPS ≥ 1 by IHC, 22C3 antibody) on archived tumor
             tissue. If CPS not available, tumors with PD-L1 TPS ≥ 1 are also eligible (but CPS
             should be performed in these cases).

          -  Incurable disease (defined as surgery and/or radiation is unable to offer curative
             potential), or ineligible for (or patient declined) local therapy.

          -  At least 18 years of age.

          -  ECOG performance status ≤ 1

          -  Normal bone marrow and organ function as defined below:

               -  Absolute neutrophil count ≥ 750/mcL

               -  Platelets ≥ 75,000/mcL

               -  Hemoglobin ≥ 9 g/L

               -  Total bilirubin ≤ 1.5 x IULN

               -  AST(SGOT)/ALT(SGPT) ≤ 3.0 x IULN

               -  Serum creatinine <1.5x ULN or Creatinine clearance ≥ 50 mL/min by Cockcroft-Gault

          -  The effects of tazemetostat on the developing human fetus are unknown. For this reason
             and because histone methyltransferase (HMT) agents are known to be teratogenic, women
             of childbearing potential and men must agree to use adequate contraception (hormonal
             or barrier method of birth control, abstinence) prior to study entry, for the duration
             of study participation, and for 6 months after the last day of treatment. Should a
             woman become pregnant or suspect she is pregnant while participating in this study,
             she must inform her treating physician immediately. Men treated or enrolled on this
             protocol must also agree to use adequate contraception prior to the study, for the
             duration of the study, and for 6 months after last day of treatment.

          -  Ability to understand and willingness to sign an IRB approved written informed consent
             document (or that of legally authorized representative, if applicable).

        Exclusion Criteria:

          -  Radiation, chemotherapy, or targeted therapy within 14 days of treatment start.

          -  Phase 2 specific: Prior therapy with an EZH2 inhibitor.

          -  Investigational therapy within 21 days of treatment start.

          -  A history of other malignancy with the exception of malignancies for which all
             treatment was completed at least 1 year before registration and the patient has no
             evidence of disease.

          -  Has known active CNS metastases. Subjects with previously treated brain metastases may
             participate provided they are stable (without any 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 14 days prior to first dose of study
             treatment.

          -  A history of allergic reactions attributed to compounds of similar chemical or
             biologic composition to tazemetostat, pembrolizumab, or other agents used in the
             study.

          -  Unable to swallow oral medication.

          -  Receiving systemic corticosteroid therapy (in doses exceeding 10 mg daily of
             prednisone equivalent) within 7 days prior to the first dose of treatment. A history
             of severe autoimmune disorder requiring high-dose corticosteroid treatment due to
             prior PD-1 inhibitor is an exclusion criterion.

          -  Uncontrolled intercurrent illness including, but not limited to, ongoing or active
             infection, symptomatic congestive heart failure, unstable angina pectoris, or cardiac
             arrhythmia.

          -  Pregnant and/or breastfeeding. Women of childbearing potential must have a negative
             serum pregnancy test within 7 days of first dose of treatment.

          -  Prior organ or allogeneic stem cell transplant.

          -  Has an active autoimmune disease (i.e. rheumatoid arthritis, lupus, Sjogren's
             syndrome) that has required IV or subcutaneous systemic treatment in the past 6 months
             (excluding Rituxan). Replacement therapy (i.e. thyroxine, insulin, or physiologic
             corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is
             not considered a form of systemic treatment.