An Exploratory Study of Pembrolizumab Plus Entinostat in Non-Inflamed Stage III/IV Melanoma

Inclusion Criteria: * Age ≥ 18 years at the time of consent. * Subject has provided informed consent and Health Insurance Portability and Accountability Act (HIPAA) prior to initiation of any study-specific activities/procedures. * Eastern Cooperative Oncology Group (ECOG) Performance Status of ≤2. * Histologically confirmed metastatic (regional or distant) melanoma of any subtype (cutaneous, mucosal, ocular). * American Joint Committee on Cancer (AJCC) stage unresectable III or stage IV disease that is measurable by RECIST v1.1 criteria. * Must agree to undergo one on-treatment tumor biopsy on day 22 (±2 days) of the study. Subjects for whom fresh samples cannot be safely provided (e.g., inaccessible tumor for biopsy or has metastatic lung lesion(s) as the only site of metastatic disease) will not be eligible for study participation. * Must have available archival tissue and subjects have consented to allow collection of archived tumor blocks from previous surgeries confirming or treating unresectable stage III or distant metastatic disease. If more than one archived tumor blocks are available, two blocks have to be analyzed for the presence of Tumor-infiltrating lymphocyte/Tumor-associated lymphocyte (TIL/TALS). Archived tumor tissues must fulfill the following criteria based on two representative Hematoxylin \& Eosin (H\&E)-stained tissue sections: (1) the tumor surface area must be at least 1cm (squared), (2) no more than 20% of necrosis, (3) the ratio of viable tumor cells to tumor-associated stroma should be at least 60/40, (4) if TILs are present based on H\&E stained sections, they must be ≤ 1% of the total number of cells in the specimen; the amount of tissue should be ≥ 1 cm2. The study pathologists must sign off on the eligibility of archived tumor blocks before study enrollment. If archival tissue is unavailable or insufficient, fresh biopsy should be performed to confirm unresectable stage III or distant metastatic disease. * Previous treatment with immune checkpoint inhibitors and chemotherapies is allowed on condition that the last treatment is at least 28 days prior to first dose of entinostat. Previous treatment with targeted therapies (e.g. Mitogen-activated protein kinase inhibitors) is allowed on condition that the last treatment was administered at least 15 days prior to first dose of entinostat). * Demonstrate adequate organ function as defined in the protocol table; all screening labs to be obtained within 21 days prior to entinostat treatment. \*Note: Hematology and other lab parameters that are ≤ grade 2 but still meet criteria for study entry are allowed. Furthermore, changes in laboratory parameters during the study should not be considered Adverse events (AEs) unless they meet criteria for dose modification(s) of study medication outlined by the protocol in Section 5.3.1 and/or worsen from baseline during therapy. * A female of childbearing potential must have a negative serum pregnancy test during screening and a negative urine pregnancy test within 3 days prior to receiving the first dose of study drug. If the screening serum test is done within 3 days prior to receiving the first dose of study drug, a urine test is not required. A female of childbearing potential must agree to use effective contraception during the study and for 120 days after the last dose of study drug. A female of non-childbearing potential defined as (by other than medical reasons): -≥45 years of age and has not had menses for \>2 years, * Amenorrheic for \<2 years without a hysterectomy and oophorectomy and a follicle-stimulating hormone value in the postmenopausal range upon pre-study (screening) evaluation, * Post hysterectomy, oophorectomy or tubal ligation. Documented hysterectomy or oophorectomy must be confirmed with medical records of the actual procedure or confirmed by an ultrasound. Tubal ligation must be confirmed with medical records of the actual procedure; otherwise the patient must be willing to use 2 adequate barrier methods throughout the study, starting with the screening visit through 120 days after the last dose of entinostat, * If male, agrees to use an adequate method of contraception starting with the first dose of study drug through 120 days after the last dose of entinostat, * See section 5.6.2 for information on acceptable methods of contraception. * Experienced resolution of toxic effect(s) of the most recent prior anti-cancer therapy to Grade ≤1 (except alopecia or neuropathy) by CTCAE v5.0. Exceptions are patients who may have developed autoimmune-type side effects that require permanent hormonal replacement from previous therapies. * If the patient underwent major surgery or radiation therapy, these procedures must have occurred at least 15 days prior to the first dose of entinostat. In addition, patients must have recovered from the toxicity and/or complications from the intervention to Grade ≤1. * Subjects must be willing and able to comply with study procedures based on the judgment of the investigator or protocol designee. Exclusion Criteria: All subjects meeting any of the exclusion criteria at baseline will be excluded from study. * Is receiving systemic steroid therapy or any other form of immunosuppressive therapy for autoimmune side effects related to previous use of immunotherapies for melanoma. Exceptions include episodic (up to 7 days) use of systemic steroids for common conditions while on study treatment (e.g. Chronic obstructive pulmonary disease (COPD) exacerbation, poison ivy), use of corticosteroids as replacement doses for adrenal or pituitary insufficiency. * Has a known history of tuberculosis (Bacillus Tuberculosis) or human immunodeficiency virus (HIV 1/2 antibodies). * Hypersensitivity to pembrolizumab or any of its excipients. Allergy to benzamide or inactive components of entinostat. * Has known history of biopsy-proven (non-infectious) pneumonitis that required systemic steroids, or any evidence of current pneumonitis. * Conditions that would preclude adequate absorption of oral medications (malabsorption, significant nausea and vomiting, resection of \>100-cm of proximal small bowel, resection of \>200-cm of distant small bowel). * Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator, including but not limited to: i. Myocardial infarction or arterial thromboembolic events within 6 months prior to screening or severe or unstable angina, New York Heart Association (NYHA) Class III of IV disease, or a QT corrected for heart rate interval \> 470 msec, ii. Uncontrolled hypertension (\>150/90 in more than 60% of recorded BP measurements taken on 5 or more separate occasions, within 3 weeks of the first dose of entinostat; at least 3 recorded measurements required on each occasion) or diabetes mellitus (HbA1c \>9.0 within 15 days from first dose of entinostat), iii. Active infection requiring systemic antibiotic therapy by the first day of entinostat treatment, iv. Known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial. * If female, is pregnant or breastfeeding, or, if male, expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment. * Known active hepatitis B (e.g., hepatitis B surface antigen-reactive) or hepatitis C (e.g., hepatitis C virus ribonucleic acid \[qualitative\]). Patients with past hepatitis B virus (HBV) infection or resolved HBV infection (defined as the presence of hepatitis B core antibody and absence of HBs Ag) are eligible. HBV DNA test must be performed in these patients prior to study treatment if known history of viral hepatitis. Patients positive for hepatitis C virus (HCV) antibody are eligible, only if polymerase chain reaction is negative for HCV RNA. * Has received a live vaccine within 30 days of planned start of study therapy. Note: Seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist®) are live-attenuated vaccines and are not allowed. * History of prior malignancy, with the exception of the following: * Non-melanoma skin cancers, non-invasive bladder cancer, and carcinoma in situ of the cervix, * Prior history of prostate cancer provided the patient is not undergoing active systemic treatment other than hormonal therapy and has documented prostate-specific antigen that is undetectable (\<0.2ng/mL), * Papillary thyroid cancer, even if patients may have just completed thyroidectomy within the last 2 years, have not received adjuvant radioactive iodine therapy, and were only recently diagnosed with asymptomatic papillary thyroid cancer and their surgery is pending, * Chronic lymphocytic leukemia (CLL) provided patient has isolated lymphocytosis (Rai stage 0) and does not require systemic treatment \[for "B" symptoms, Richter's transformation, lymphocyte doubling time (\<6 months), lymphadenopathy or hepatosplenomegaly\], * Lymphoma, hairy-cell leukemia, or myelodysplasia, provided that patient is not on active systemic treatment and is in complete remission, as evidenced by positron emission tomography/computerized tomography (PET/CT) scans and bone marrow biopsies for at least 3 months, * History of any other malignancy provided patient has completed therapy and is free of disease for ≥ 2 years. If patient had other malignancy within the last 2 years from which he, or she, may have been completely cured by surgery alone, he may be considered to be enrolled on condition that the risk of development of distant metastatic disease based on the most recent AJCC staging system is less than 30%. * Has known active (i.e. previously untreated) parenchymal central nervous system (CNS) metastases that are symptomatic, and/or more than one lesion with the largest diameter being \> 5-mm and/or require antiepileptic drugs or systemic corticosteroids for management of intracranial symptoms. Patients with carcinomatous meningitis are also excluded. Exceptions are: * Subjects with previously treated brain metastases provided they are stable (i.e. without evidence of progression by brain Magnetic Resonance Imaging (MRI) or head CT with IV contrast) for at least 2 weeks prior to the first dose of entinostat. Any neurologic symptoms must have returned to baseline, and have no evidence of new or enlarging brain metastases, and are not using ongoing systemic corticosteroids for management of intracranial symptoms for at least 7 days prior to first dose of entinostat, * Patients with active (i.e. not treated with stereotactic radiosurgery), single, asymptomatic, up to 5-mm in largest diameter brain metastases (measured either by brain MRI with IV contrast or head CT with IV contrast measuring within 2 weeks prior to the first dose of entinostat). * Currently participating and receiving study therapy or has 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 entinostat. * Subject is receiving prohibited medications or treatments as listed in section 5.5 of the protocol that cannot be discontinued/replaced by an alternative therapy. * Prior treatment with Histone/deacetylase inhibitor (HDACi) for their melanoma.