Study of Front Line Pembrolizumab and Valemetostat in PD-L1 Positive, HPV-Negative Recurrent/Metastatic Squamous Cell Carcinoma (SCC) of the Head and Neck: The PANTHERAS

-INCLUSION CRITERIA: Participants must have a diagnosis of one of the following types of cancer: Phase Ib (Part A): -Histologically or cytologically confirmed locoregionally recurrent or metastatic (R/M) human papillomavirus (HPV)-negative* or -positive* squamous cell carcinoma of the head and neck: oral cavity, tonsil, pharynx, hypopharynx, larynx. Note: Nasopharyngeal carcinoma and cutaneous squamous cell carcinoma (SCC) are excluded. OR -Histologically or cytologically confirmed R/M sinonasal carcinomas of the head and neck. OR -Histologically confirmed R/M squamous non-small cell lung cancer (NSCLC). *HPV status will be determined by history of p16 IHC staining conducted per standard of care. Phase II (Part B): -Histologically or cytologically confirmed locoregionally R/M HPV-negative* squamous cell carcinoma of the head and neck: oral cavity, tonsil, pharynx, hypopharynx, larynx. Note: Nasopharyngeal carcinoma and cutaneous SCC are excluded. *HPV status will be determined by history of p16 IHC staining conducted per standard of care. PD-L1 combined positive score (CPS) >= 1, confirmed by Food and Drug Administration (FDA) approved 22C3 PharmDx test. Phase Ib only: Participants may be na(SqrRoot) ve or refractory to pembrolizumab or other PD- L1/PD-1 checkpoint inhibitors and may have had any number of lines of systemic therapy. Phase II only: Participants must be pembrolizumab-naive and not have received PD- L1/PD-1 checkpoint inhibitors and must not have had prior lines of systemic chemotherapy or immunotherapy for recurrent or metastatic HNSCC. Age >=18 years. Eastern Cooperative Oncology Group (ECOG) performance status <=2 (Phase Ib) or <= 1 (Phase II). Participants must have adequate organ and marrow function as defined below: 7.1 Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) <=3.0 X upper limit of normal (ULN) 7.2 Total bilirubin <=1.5 X ULN. Note: Participants with Gilbert's syndrome may have total bilirubin <3.0 mg/dL 7.3 Absolute neutrophil count (ANC) >=1.5 X 10^9/L 7.4 Hemoglobin (Hgb) >=8.5 g/dL 7.5 Platelet count >=75 X 10^9/L 7.6 Creatinine clearance >=60 mL/min (calculated by the Cockcroft-Gault equation). Acute non-hematologic toxic effects (as evaluated by NCI Common Terminology Criteria for Adverse Events (CTCAE), version 5.0 of any prior therapy (except alopecia) resolved as shown below: 8.1 Peripheral motor neuropathy, Peripheral sensory neuropathy: Grade <=2 8.2 Fatigue: Grade <=2 8.3 All others: Grade <=1 Participants with treated brain metastases are eligible if follow-up brain imaging after central nervous system (CNS)-directed therapy shows no evidence of progression within 4 weeks before study treatment initiation. Participants with new or progressive brain metastases (active brain metastases) or leptomeningeal disease are eligible if the treating physician determines that immediate CNS specific treatment is not required per Standard of Care. Participants must have measurable disease by RECIST 1.1. Human immunodeficiency virus (HIV)-infected participants on effective anti-retroviral therapy with undetectable viral load are eligible for this trial. For participants with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated. Participants with a history of current HCV infection who are currently on treatment must have an undetectable HCV viral load to be eligible. Women of child-bearing potential (WOCBP) must agree to use a highly effective method of contraception (hormonal, intrauterine device (IUD), surgical sterilization, abstinence) for the duration of the study treatment and up to 4 months after the last dose of the study drug(s). A female is considered of childbearing potential following menarche and until becoming postmenopausal (no menstrual period for a minimum of 12 months) unless permanently sterile (undergone a hysterectomy, bilateral salpingectomy, or bilateral oophorectomy) with surgery at least 1 month before the first dose of study drug(s) or confirmed by follicle-stimulating hormone (FSH) test >40 mIU/mL and estradiol <40 pg/mL (<140 pmol/L). Men must agree to use an effective method of contraception (barrier, surgical sterilization, abstinence) for the duration of the study treatment and up to 4 months after the last dose of the study drug(s). We also will recommend men with female partners of childbearing potential to ask female partners to be on highly effective birth control (hormonal, intrauterine device (IUD), surgical sterilization). Female participants must not donate, or retrieve for their own use, ova from the time of study treatment initiation and throughout the study treatment period, and for at least 4 months after the final study drug(s) administration. Male participants must not freeze or donate sperm within the same period. Breastfeeding participants must be willing to discontinue breastfeeding from study treatment initiation through 4 months after the last dose of the study drug(s). Participants must have disease amenable for biopsies (not used for evaluation of disease per RECIST 1.1) and be willing to undergo these biopsies (Phase II only). The ability of a participant to understand and the willingness to sign a written informed consent document. EXCLUSION CRITERIA: History of allergic reactions attributed to compounds of similar chemical or biologic composition to valemetostat or pembrolizumab used in the study. Prior curative radiation therapy or major surgery within 4 weeks or palliative radiation therapy within 2 weeks prior to the first dose of study drug(s). Prior systemic therapy (e.g., chemotherapy, immunomodulatory therapy, monoclonal antibody therapy, or investigational therapy) within 4 weeks, or 5 half-lives of the drug, whichever is longer, prior to the first dose of the study drug(s). History of previous treatment with EZH2 inhibition. Participants currently receiving any medications or substances that are moderate or strong inducers or moderate or strong inhibitors of cytochrome P450 (CYP3A). Participants currently receiving any medications or substances that are P-gp inhibitors (e.g., amiodarone, clarithromycin, diltiazem, erythromycin, ketoconazole, itraconazole, propafenone, quinidine, and verapamil). Consumption of foods and beverages that are strong CYP3A inhibitors or inducers (star fruit, Seville orange, Seville orange-containing foods and beverages, grapefruit, grapefruit-containing food or beverages) within 3 days prior to the first dose of study drug(s). Active immunosuppressive treatment equivalent to>10 mg of prednisone daily. Note: Short-course systemic corticosteroids (e.g., prevention/treatment for transfusion reaction) or use for a non-cancer indication (e.g., adrenal replacement) is acceptable. Cardiovascular diseases with the following criteria: 9.1 Evidence of prolongation of QT/corrected (QTc) interval (e.g., repeated episodes of QT corrected for heart rate using Fridericia s method [QTcF] >470 ms regardless of sex) (average of triplicate determinations) at screening 9.2 Diagnosed or suspected long QT syndrome, or known family history of long QT syndrome 9.3 History of clinically relevant ventricular arrhythmias, such as ventricular tachycardia, ventricular fibrillation, or Torsade de pointes 9.4 Uncontrolled arrhythmia (participants with asymptomatic, controllable atrial fibrillation may be enrolled), or asymptomatic persistent ventricular tachycardia at screening 9.5 Participant has clinically relevant bradycardia of less than 50 bpm at screening unless the participant has a pacemaker 9.6 History of second- or third-degree heart block. Candidates with a history of heart block may be eligible if they currently have pacemakers, and have no history of fainting or clinically relevant arrhythmia with pacemakers, within 6 months prior to treatment initiation 9.7 Myocardial infarction within 6 months prior to treatment initiation 9.8 Angioplasty or stent graft implantation within 6 months prior to treatment initiation 9.9 Uncontrolled angina pectoris within 6 months prior to treatment initiation 9.10 History of New York Heart Association (NYHA), https://www.merckmanuals.com/professional/multimedia/table/new-york-heart- association-nyha-classification-of-heart-failure) Class 3 or 4 congestive heart failure 9.11 Coronary/peripheral artery bypass graft within 6 months prior to treatment initiation 9.12 Uncontrolled hypertension (resting systolic blood pressure >180 mmHg or diastolic blood pressure >110 mmHg) at screening 9.13 Complete left bundle branch block at screening History of autoimmune disease with the exception of controlled thyroid disease, psoriasis not requiring medications, vitiligo, and alopecia. Prior malignancy active within the previous 2 years except for locally curable cancer that is currently considered as cured and does not require additional Standard of Care treatment, such as cutaneous basal or squamous cell carcinoma, superficial bladder cancer, or cervical carcinoma in situ, or an incidental histological finding of prostate cancer. Ongoing uncontrolled systemic bacterial, fungal, or viral infection currently requiring treatment with intravenous antibiotics, antivirals, or antifungals. Pregnancy (confirmed with beta-human chorionic gonadotropin (beta-HCG) serum or urine pregnancy test performed in females of childbearing potential at screening). Uncontrolled intercurrent illness or situations that would limit compliance with study requirements.