Window of Opportunity Study of Pembrolizumab Alone and in Combinations in Bladder Cancer

Inclusion Criteria: * Written informed consent obtained to participate in the study and HIPAA authorization for release of personal health information. * Subjects must agree to donate tumor tissue from their transurethral resection of the bladder tumor (TURBT) and from their cystectomy, as well as agree to donate whole blood prior to initiating therapy, and at cystectomy. * Age ≥18 years at the time of consent. * Eastern Cooperative Oncology Group performance status of ≤ 2. * Histological confirmation of urothelial carcinoma of the bladder; those with mixed histology, including a component of urothelial carcinoma, are eligible. Pure small cell carcinoma, pure adenocarcinoma, and pure squamous cell carcinoma are excluded. * Subject has clinical stage T2-T4a N0/X M0 urothelial carcinoma. Clinical T stage is based on the pre-study standard of care transurethral resection of the bladder tumor (TURBT) sample and imaging studies (abdominal/pelvic CT or MRI scan and CT scan of the chest performed within 4 weeks prior to treatment initiation). * Available formalin-fixed paraffin-embedded (FFPE) archival tumor specimen that contains sufficient tissue to generate at least 15 (preferably 20) unstained slides, each with tissue sections that are 5 - 10 microns thick. * Subject is planned to undergo definitive surgery (radical cystectomy). * Subject demonstrates adequate organ function as defined by the protocol; all screening laboratory assessments should be performed within 10 days of treatment initiation. * Subject refuses to receive or is ineligible to receive cisplatin-based neoadjuvant chemotherapy. Determination of ineligibility for cisplatin is based on at least one of the following criteria: * Eastern Cooperative Oncology Group performance status of 2 * Glomerular filtration rate (GFR) per Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation ≤ 60 mL/min * NCI CTCAE v5.0 Grade ≥ 2 hearing loss * NCI CTCAE v5.0 Grade ≥ 2 neuropathy * Female subjects of childbearing potential should have a negative serum pregnancy within 72 hours prior to receiving the first dose of the study treatment. * Female subjects of childbearing potential must be willing to use an adequate method of contraception as outlined in the protocol, for the course of the study through 120 days after the last dose of study medication. Note: Abstinence is acceptable if this is the usual lifestyle and preferred contraception for the subject. -Male subjects of childbearing potential must agree to use an adequate method of contraception as outlined in the protocol, 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 subject. * Subject is able to tolerate and retain oral medication. * Life expectancy greater than 3 months. Exclusion Criteria: * Subject is currently participating in or has participated in a study of an investigational agent or using an investigational device within 4 weeks of the first dose of pembrolizumab. * Subject has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment. Inhaled and topical steroids are allowed. * Subject has a known history of active tuberculosis. * Subject has known hypersensitivity to pembrolizumab or any of its excipients. * For subjects in arm 2 only, to benzamide or inactive ingredients of entinostat. * Subject has a known additional malignancy that is progressing or requires active treatment. Exceptions include basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or in situ cervical cancer that has undergone potentially curative therapy. * Subject has 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). 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. * Subject has a history of (non-infectious) pneumonitis that required steroids or a current pneumonitis. * Subject has an active infection requiring systemic therapy. * Subject 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. Please note that subjects with Grade ≥2 peripheral neuropathy, are allowed on this study. * Subject has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial. * Subject is pregnant or breastfeeding or 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. * Subject has received prior therapy with an anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CD137, or anti-cytotoxic T-lymphocyte-associated antigen-4 (CTLA-4) antibody (including ipilimumab or any other antibody or drug specifically targeting T-cell co-stimulation or checkpoint pathways). * Subject has had prior systemic cytotoxic chemotherapy for urothelial carcinoma (prior intravesicular chemotherapies are permitted). * Subject is receiving histone deacetylase inhibitors, including valproic acid, DNA methyltransferase inhibitors. * For subjects in arm 2 only, subject is receiving drugs that are known to inhibit or induce P-gp. * For subjects in arm 2 only, subject has gastrointestinal impairment that may significantly affect absorption of entinostat, such as ulcerative disease, malabsorption syndrome, and a history of small bowel resection. * Subject has received prior radiation therapy to the bladder for the purpose of treating urothelial carcinoma. * Subject has a known history of Human Immunodeficiency Virus (HIV) (HIV 1/2 antibodies). * Subject has known history of Hepatitis B (e.g., HBsAg reactive) or Hepatitis C (e.g., HCV RNA \[qualitative\] has been detected). * Subject has received a live vaccine within 30 days prior to the first dose of study drug. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster (chicken pox), yellow fever, rabies, Bacillus Calmette-Guérin (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (e.g., FluMist®) are live attenuated vaccines and are not allowed. * For subjects in arm 2 only, subject uses drugs or herbal supplements that are known sensitive cytochromes P450 (CYP) substrates of CYP1A2, CYP2C8, CYP3A with narrow therapeutic range