Inclusion Criteria:

          -  Patients in Arm A may begin treatment after this registration

          -  Patients in Arm B will be required to undergo a second registration by meeting PD-L1
             eligibility criteria. A tissue sample must be submitted for central analysis of PD-L1
             after eligibility are confirmed

          -  Patients must have pathologically confirmed urothelial carcinoma

               -  Note: patients with mixed histology (with predominant urothelial carcinoma) are
                  eligible

          -  Patients must have locally advanced or metastatic disease with either:

               -  Arm A: disease progression during or following (within 12 months) platinum-based
                  chemotherapy (cisplatin or carboplatin)

                    -  Note: no minimum number of cycles on platinum-based chemotherapy are
                       required. Patients who have had multiple rounds of platinum-based
                       chemotherapy with events of intermittent progressive disease (PD) are
                       eligible as long as progression has been confirmed while on or within 12
                       months from platinum based therapy OR

               -  Arm B: cisplatin ineligible as defined

                    -  Patients in Arm B must also

                         -  Undergo central analysis of tissue for PD-L1 status

                         -  Be positive for PD-L1

                         -  If archival tissue is unavailable or insufficient for PD-L1 central
                            analysis, a new biopsy must be performed Alternatively, patients who
                            previously have had PD-L1 testing performed as standard of care via the
                            Food and Drug Administration (FDA)-approved Dako PD-L1
                            immunohistochemistry (IHC) 22C3 PharmDx Assay companion diagnostic test
                            and who have a combined positive score (CPS) of >= 10 may be eligible.
                            In these cases, PD-L1 testing does not need to be repeated, and tissue
                            does not need to be sent for central analysis

          -  All patients must have measurable disease in accordance with RECIST criteria version
             (v) 1.1

               -  Note: radiological evaluation should occur within 28 days prior to study
                  registration

          -  Patients must be naive to prior PD-L1 or EZH2 inhibitors

               -  Note: patients in Arm A should have received platinum-based chemotherapy only

          -  ECOG performance status =< 2

          -  Patients must have a blood smear or manual differential performed at screening showing
             no significant morphologic abnormalities on complete blood count (CBC) testing

          -  Leukocytes >= 3000/mcL (performed within 14 days prior to registration)

          -  Absolute neutrophil count (ANC) >= 1500/mcL (performed within 14 days prior to
             registration)

          -  Platelets >= 100 000/mcL (performed within 14 days prior to registration)

          -  Hemoglobin >= 9 g/dL or >= 4.9 mmol/L (performed within 14 days prior to registration)

          -  Creatinine =< 1.5 x upper limit of normal (ULN) OR measured or calculated creatinine
             clearance (CrCl) >= 30 mL/min for patient with creatinine levels > 1.5 x institutional
             ULN (performed within 14 days prior to registration)

               -  Creatinine clearance (CrCl) should be calculated per institutional standard

               -  Glomerular filtration rate (GFR) can also be used in place of creatinine or CrCl

          -  Total bilirubin =< 1.5 x ULN OR direct bilirubin =< ULN for patients with total
             bilirubin levels > 1.5 x ULN (performed within 14 days prior to registration)

          -  Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase [SGOT]) and
             alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) =< 2.5 x
             ULN OR =< 5 x ULN for patients with liver metastases (performed within 14 days prior
             to registration)

          -  International normalized ratio (INR) or prothrombin time (PT) =< 1.5 x ULN unless
             patient is receiving anticoagulant therapy as long as PT or partial thromboplastin
             time (PTT) is within therapeutic range of intended use of anticoagulants (performed
             within 14 days prior to registration)

          -  Activated partial thromboplastin time (aPTT) =< 1.5 x ULN unless patient is receiving
             anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use
             of anticoagulants (performed within 14 days prior to registration)

          -  The effects of pembrolizumab (MK-3475) and tazemetostat on the developing human fetus
             are unknown. For this reason and because PD-1 inhibitors as well as EZH2 inhibitors
             are known to be teratogenic, women of child-bearing potential and men must agree to
             use adequate contraception (hormonal or barrier method of birth control; abstinence)
             prior to study entry and for the duration of study participation. Female patients of
             childbearing potential must have a negative urine or serum pregnancy test within 72
             hours prior to receiving the first dose of study medication. If the urine test is
             positive or cannot be confirmed as negative, a serum pregnancy test will be required.

               -  Female patients of childbearing/reproductive potential must be willing to use an
                  adequate method of contraception, for the course of the study through 6 months
                  after the last dose of study medication. Note: Abstinence is acceptable if this
                  is the usual lifestyle and preferred contraception for the patient

               -  Male patients of reproductive potential must agree to use an adequate method of
                  contraception, starting with the first dose of study therapy through 120 days
                  after the last dose of study therapy. Note: Abstinence is acceptable if this is
                  the usual lifestyle and preferred contraception for the patient.

               -  Should a woman become pregnant or suspect she is pregnant while she or her
                  partner is participating in this study, she should inform her treating physician
                  immediately.

          -  Participants who have the ability to understand and the willingness to sign an
             Institutional Review Board (IRB) approved written informed consent document are
             eligible OR Participants with impaired decision-making capacity (IDMC) who have a
             legally authorized representative (LAR) or caregiver are eligible

          -  Human immunodeficiency virus (HIV)-infected patients who do not have a history of
             Kaposi sarcoma and/or Multicentric Castleman Disease, who are on effective
             anti-retroviral therapy, and who have undetectable viral load within 6 months are
             eligible for this trial

        Exclusion Criteria:

          -  Patients with disease that is suitable for local therapy administered with curative
             intent are not eligible

          -  Patients who have had chemotherapy, targeted small molecule therapy, or radiotherapy
             within 4 weeks prior to entering the study are not eligible

          -  Patients who have not recovered from adverse events due to prior anti-cancer therapy
             (i.e., have residual toxicities > grade 1 per Common Terminology Criteria for Adverse
             Events [CTCAE] v.5 ) are not eligible

               -  Note: patients with =< grade 2 neuropathy or =< grade 2 alopecia or =< grade 3
                  audiometric hearing loss are an exception to this criterion and may qualify for
                  the study

               -  Note: if patients received major surgery, they must have recovered adequately
                  from the toxicity and/or complications from the intervention prior to starting
                  therapy

          -  Patients are not eligible who are currently participating and receiving study therapy
             or have participated in a study of an investigational agent and received study therapy
             or used an investigational device within 4 weeks of the first dose of treatment

          -  Patients who have received transfusion of blood products (including platelets or red
             blood cells) or administration of colony stimulating factors (including granulocyte
             colony-stimulating factor [G-CSF], granulocyte macrophage colony-stimulating factor
             [GM-CSF], or recombinant erythropoietin) within 4 weeks prior to the first dose of
             treatment are not eligible

          -  Patients with a diagnosis of immunodeficiency or are receiving systemic steroid
             therapy or any other form of immunosuppressive therapy within 7 days prior to the
             first dose of trial treatment are not eligible

               -  Note: the use of physiologic doses of corticosteroids may be approved after
                  consultation with the study principal investigator (PI)

          -  Patients with thrombocytopenia, neutropenia, or anemia of grade 3 (per CTCAE 5.0
             criteria) are not eligible

          -  Patients with 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 are not eligible

          -  Patients with an ongoing or untreated hematologic malignancy or myeloproliferative
             disorder, or a prior history of a hematologic malignancy or myeloproliferative
             disorder are not eligible. (Examples of excluded malignancies/disorders include but
             are not limited to myelodysplastic syndrome [MDS], T cell lymphoblastic lymphoma
             (T-LBL), T cell acute lymphoblastic leukemia (T-ALL), and any other myeloid or
             lymphoid malignancy)

          -  Patients who have received prior PD-L1/PD-1/PD-L2 or EZH2 inhibitor therapy are not
             eligible

          -  Patients who have had a prior monoclonal antibody within 4 weeks prior to study day 1
             are not eligible

          -  Patients must be disease-free of prior invasive malignancies for > 5 years, with the
             exception of curatively-treated basal cell or squamous cell carcinoma of the skin or
             carcinoma in situ of the cervix. If there is a history of prior malignancy, patients
             must not be receiving other specific treatment for that cancer

          -  Patients with known brain metastases or carcinomatous meningitis are excluded from
             this clinical trial because of their poor prognosis and because they often develop
             progressive neurologic dysfunction that would confound the evaluation of neurologic
             and other adverse events

               -  Note: patients with previously treated brain metastases may participate provided
                  they are stable (without evidence of progression by imaging using the identical
                  imaging modality for each assessment, either magnetic resonance imaging [MRI] or
                  computed tomography [CT] scan, for at least 4 weeks prior to the first dose of
                  trial treatment and any neurologic symptoms have returned to baseline), have no
                  evidence of new or enlarging brain metastases, and are not using steroids for at
                  least 7 days prior to trial treatment

          -  Patients with a history of allergic reactions attributed to compounds of similar
             chemical or biologic composition to pembrolizumab (MK-3475) or tazemetostat are not
             eligible

          -  Patients with an active autoimmune disease that has required systemic treatment in the
             past 2 years (i.e., with use of disease modifying agents, corticosteroids, or
             immunosuppressive drugs) are not eligible

               -  Note: replacement therapy (e.g., thyroxine, insulin, or physiologic
                  corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.)
                  is not considered a form of systemic treatment

          -  Patients with a history of (non-infectious) pneumonitis that required steroids or
             current pneumonitis are not eligible

          -  Patients with a prolongation of corrected QT interval (Fridericia's correction formula
             [QTcF]) of > 450 msec are not eligible

          -  Patients with major surgery within 3 weeks before the first dose of study drugs

               -  Note: minor surgery (e.g. minor biopsy of an extracranial site, central venous
                  catheter placement, shunt revision) has no restriction

          -  Patients must not have a history or current evidence of any condition, therapy, or
             laboratory abnormality that might confound the results of the trial, interfere with
             the patient's participation for the full duration of the trial, or is not in the best
             interest of the patient to participate, in the opinion of the treating investigator

          -  Patients receiving any medications or substances that are strong inhibitors or
             inducers of CYP3A =< 14 days prior to study treatment are not eligible

               -  Note: The study team should check a frequently-updated medical reference for a
                  list of drugs to avoid or minimize use of. As part of the enrollment/informed
                  consent procedures, the patient will be counseled on the risk of interactions
                  with other agents, and what to do if new medications need to be prescribed or if
                  the patient is considering a new over-the-counter medicine or herbal product

          -  Patients who are unable to take oral medication OR have malabsorption syndrome or any
             other uncontrolled gastrointestinal condition (e.g., nausea, diarrhea, vomiting) that
             might impair the bioavailability of tazemetostat are not eligible

          -  Patients with uncontrolled intercurrent illness including, but not limited to, ongoing
             or active infection, interstitial lung disease or active, non-infectious pneumonitis,
             symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia,
             uncontrolled arterial hypertension, stroke within 6 months prior to starting study
             treatment, or psychiatric illness/social situations that would limit compliance with
             study requirements are not eligible

          -  Pregnant women are excluded from this study because pembrolizumab (MK-3475) and
             tazemetostat are agents with the potential for teratogenic or abortifacient effects.
             Because there is an unknown but potential risk for adverse events in nursing infants
             secondary to treatment of the mother with pembrolizumab (MK-3475) and tazemetostat,
             breastfeeding should be discontinued if the mother is treated with pembrolizumab
             (MK-3475) or tazemetostat

               -  Pembrolizumab (MK-3475) may have adverse effects on a fetus in utero.
                  Furthermore, it is not known if pembrolizumab (MK-3475) has transient adverse
                  effects on the composition of sperm. Patients are excluded from this study if
                  pregnant or breastfeeding, or expecting to conceive or father children within the
                  projected duration of the trial, starting with the screening visit through 6
                  months after the last dose of trial treatment

          -  Patients with a known history of hepatitis B (defined as hepatitis B surface antigen
             [HBsAg] reactive) or known hepatitis C virus (defined as HCV ribonucleic acid [RNA]
             [qualitative] is detected) infection are not eligible

               -  Note: no testing for hepatitis B and hepatitis C is required unless mandated by
                  local health authority

          -  Patients who have received a live vaccine within 30 days of planned treatment start
             are not eligible

               -  Note: seasonal flu vaccines that do not contain live virus are permitted

          -  PD-L1 ELIGIBILITY (ARM B ONLY):

          -  Patients in Arm B must have positive PD-L1 status as confirmed by central analysis
             prior to second step registration and treatment initiation

               -  NOTE: positive PD-L1 expression is defined as a combined positive score (CPS) >=
                  10 and will be confirmed in a report from HistoGeneX.

        Alternatively, patients who previously have had PD-L1 testing performed as standard of care
        via the FDA-approved Dako PD-L1 IHC 22C3 PharmDx Assay companion diagnostic test and who
        have a combined positive score (CPS) of >= 10 may be eligible. In these cases, PD-L1
        testing does not need to be repeated, and tissue does not need to be sent for central
        analysis