Phase 1b Study of TMV Vaccine Therapy Alone and TMV Vaccine Plus Pembrolizumab for Recurrent and/or Metastatic Head and Neck Squamous Cell Carcinoma (HNSCC)

Inclusion Criteria: * Must be at least ≥ 18 years of age * Histologically proven squamous cell carcinoma of the head and neck (HNSCC), amenable to salvage surgery. p16 positive and negative allowed. Squamous cell carcinoma of the oral cavity, larynx, hypopharynx, oropharynx, nasopharynx, sinonasal carcinoma and cancer of unknown primary (squamous cell carcinoma only) are all allowed. They will be allowed to have up to 3 different regimens after diagnosed of recurrent or metastatic HNSCC * Oropharyngeal tumors must have p16 or human papillomavirus (HPV) testing done * The tumor tissues must be available and banked (- 80°C) at the time of salvage surgery (1st informed consent form \[ICF\] must be signed) * Recurrent and/or metastatic HNSCC that has failed standard chemotherapy and immunotherapy. Eligible subjects must have progressed on ≥ 2 lines of standard of care prior to starting trial therapy. For patients who have relapsed within 6 months of systemic therapy given with curative intent, that therapy will count as a line of metastatic therapy. Eligible subjects will have no restriction on prior lines of therapy in the metastatic/advanced disease setting * The tumors should be measurable by Response Evaluation Criteria in Solid Tumors (RECIST) criteria * Must have enough tissue collected after salvage surgery to make at least 3 doses of vaccine (minimum weight of the resectable tumor tissue is ≥ .5 grams) and adequate cellularity (\> 40% cellularity) assessed by the head and neck pathologists * Eastern Cooperative Oncology Group (ECOG) performance status 0, 1 or 2 * Absolute neutrophil count ≥ 1,500 cells/uL * Platelets ≥ 100,000/uL * Hemoglobin ≥ 9.0g/dL (may receive packed red blood cell \[prbc\] transfusion) * Total bilirubin ≤ 1.5 x the upper limit of normal (ULN) * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 2.5 x ULN * Albumin ≥ 3.0 g/dL * Serum creatinine ≤ 1.5 x ULN * Calculated creatinine clearance of ≥ 50 mL/min * International normalized ratio (INR) ≤ 1.5. Anticoagulation is allowed only with low molecular weight heparin (LMWH). Patient receiving low molecular weight (LMW) heparin on stable therapeutic dose for more than 2 weeks or with factor Xa level \< 1.1U/mL are allowed on the trial * Willingness and ability to comply with scheduled visits, treatment plans, laboratory tests, and other study procedures * Ability to understand and willingness to sign written informed consent documents * Female subjects of childbearing potential must agree to use adequate contraception (e.g., hormonal or barrier method of birth control; abstinence) for the duration of study treatment and 3 months after completion * Male subjects must agree to use adequate contraception (e.g., condoms; abstinence) for the duration of study treatment and 3 months after completion * Female subjects of childbearing age must have a negative serum pregnancy test at study entry * Patients who have received prior pembrolizumab are eligible Exclusion Criteria: * Salivary tumors and non-squamous cell histology in head and neck cancer * Not enough tissue collected after surgery for a planned 3 doses (weight of the resectable tumor tissue is less than 1.0 gram) * Treatment with chronic immunosuppressants (e.g., cyclosporine following transplantation) * Prior organ allograft or allogeneic bone marrow transplantation * Subjects with any active autoimmune disease or history of known or suspected autoimmune disease except for subjects with vitiligo, resolved childhood asthma/atopy, type I diabetes mellitus, residual hypothyroidism due to autoimmune condition only requiring hormone replacement, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger are permitted to enroll * Subjects with a condition requiring systemic treatment with either corticosteroids (\> 10mg daily prednisone equivalents) or other immunosuppressive medications within 14 days of study drug administration. Inhaled or topical steroids and adrenal replacement doses \> 10mg daily prednisone equivalents are permitted in the absence of active autoimmune disease * Women who are pregnant or lactating, and child-bearing potential women without adequate contraception * Uncontrolled intercurrent illness including, but not limited to, human immunodeficiency virus (HIV)-positive subjects receiving combination antiretroviral therapy, ongoing or active infection, symptomatic congestive heart failure (New York Heart Association \[NYHA\] class III or IV), unstable angina pectoris, ventricular arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Other medications, or severe acute/chronic medical or psychiatric condition, or laboratory abnormality that may increase the risk associated with study participation or study drug administration, or may interfere with the interpretation of study results, and in the judgment of the investigator would make the subject inappropriate for entry into this study * Clinical evidence of bleeding diathesis or coagulopathy * Patients with prior malignancies, including pelvic cancer, are eligible if they have been disease free for \> 5 years. Patients with prior in situ carcinomas are eligible provided there was complete removal * Active bacterial or fungal infections requiring systemic treatment within 7 days of treatment * Use of other investigational drugs (drugs not marked for any indication) within 28 days or at least 5 half-lives (whichever is longer) before study drug administration * History of severe hypersensitivity reactions to other monoclonal antibodies * Non-oncology vaccines within 28 days prior to planned treatment