Pembrolizumab and Vorinostat in Treating Patients With Recurrent Squamous Cell Head and Neck Cancer or Salivary Gland Cancer That Is Metastatic and/or Cannot Be Removed by Surgery

Inclusion Criteria

• Phase I run in: biopsy proven RMHNSCC with the following primary sites: nasopharynx, paranasal sinus, nasal cavity, skin/cutaneous sites; patients with unknown head and neck primary sites will be enrolled; patients with recurrent or metastatic squamous cell carcinomas of the head and neck (regardless of primary site) who are either unwilling to receive or have contraindications (deemed by treating physician) to standard systemic chemotherapy will also be eligible; patients with biopsy proven RMSGC be eligible as well
• Phase II expansion: biopsy proven RMHNSCC, of any primary site (including unknown primary) and RMSGC will be eligible
• Have evidence of disease progression by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria within 3 months prior to study enrollment; if the patient was receiving a prior line of systemic therapy, he/she should have evidence of disease progression on that line of treatment prior to enrollment
• Have received any number lines of prior systemic therapy (including systemic therapy in the curative intent setting)
• Be willing and able to provide written informed consent for the trial and comply with the study visit requirements
• Have measurable disease based on RECIST 1.1
• Have provided tissue from an archival tissue sample or newly obtained core or excisional biopsy of a tumor lesion
• Have a performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG) performance scale
• Absolute neutrophil count (ANC) >= 1,500/mcL
• Platelets >= 100,000/mcL
• Hemoglobin >= 9 g/dL or >= 5.6 mmol/L
• Serum creatinine = = 60 mL/min for subject with creatinine levels > 1.5 x institutional ULN (glomerular filtration rate [GFR] can also be used in place of creatinine or creatinine clearance [CrC])
• Creatinine clearance should be calculated per institutional standard
• Serum total bilirubin = 1 year
• Male subjects should 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
• Patient is 2 year; male subjects should 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
• Does not have a history or current evidence of any condition, therapy, or laboratory abnormality that might 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

Exclusion Criteria

• 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 treatment
• 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
• Has had a prior monoclonal antibody within 4 weeks prior to study day 1 or who has not recovered (i.e., =< grade 1 or at baseline) from adverse events due to agents administered more than 4 weeks earlier
• Has had prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to study day 1 or who has not recovered (i.e., =< grade 1 or at baseline) from adverse events due to a previously administered agent
• Note: subjects with =< grade 2 neuropathy are an exception to this criterion and may qualify for the study
• Note: if subject received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy
• 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
• Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis; subj