TA-CIN Vaccine With Anti-PD-1 Therapy in Recurrent HPV16-associated Cancers

Inclusion Criteria: 1. Age ≥ 18 years 2. Diagnosis with one of the following: 1. Unresectable recurrent and/or metastatic cervical cancer with disease progression on or after chemotherapy whose tumors express PD-L1 \[Combined Positive Score (CPS) 1\] as determined by an FDA-approved test. 2. Unresectable recurrent and/or metastatic head and neck squamous cell cancer (HNSCC) in either of the following settings: i.) The tumor expresses PD-L1 \[Combined Positive Score (CPS) 1\] as determined by an FDA-approved test and the patient has received no prior therapy, or ii.)The patient has experienced disease progression on or after platinum-containing chemotherapy. c)Metastatic anal cancer that has progressed after prior chemotherapy. 3. Eligible for and planning to start therapy with anti-PD-1 therapy based on NCCN guidelines, such as pembrolizumab, every 3 weeks according to standard of care. 4. Documented to have HPV16 nucleic acid within the tumor specimen as determined by in situ hybridization. NOTE: HPV16 nucleic acid testing may be done as part of a "pre-screening" consent at any time prior to enrollment on the primary study. Archival tissue will be used to perform this test. To be eligible for HPV16 testing on study, patients must have cancer not amenable to curative therapy and be a candidate for anti-PD-1/PD-L1 antibody therapy. 5. Measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) guideline (version 1.1) Appendix D, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as ≥20 mm (≥2 cm) by chest x-ray or as ≥10 mm (≥1 cm) with CT scan, MRI, or calipers by clinical exam. 6. A minimum of one injectable lesion at least 1 cm in size as determined by the investigator (for superficial tumors) or radiologist (deep tumors). Lesions in previously irradiated areas may be considered target lesions if progression has been demonstrated. 7. Must have adequate organ and marrow function as defined below: Screening Organ and Marrow Function Criteria * absolute neutrophil count ≥1,000/mcL * absolute lymphocyte count ≥500/mcL * platelets ≥100,000/mcL * total bilirubin ≤1.5 × institutional upper limit of normal (ULN) * AST(SGOT) ≤1.5 × institutional ULN * ALT(SGPT) ≤1.5 × institutional ULN * INR ≤1.8 if not on Coumadin, or if on Coumadin, within therapeutic target range and able to discontinue temporarily for study procedures * creatinine OR glomerular filtration rate (GFR) ≤1.5 × institutional ULN * 60 mL/min/1.73 m2 per Modified Cockcroft-Gault Formula 8. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 9. Ability to understand and the willingness to sign a written informed consent document 10. For patients with childbearing capacity, agreement (by patient) to use highly effective forms of contraception (i.e., one that results in a low failure rate \[\< 1% per year\] when used consistently and correctly) and to continue its use at least 90 days post last dose of anti-PD-1/PD-L1 antibody therapy. 11. Subject is able to adhere to the study visit schedule and other protocol requirements Exclusion Criteria: 1. Patients with a diagnosis of immunosuppression or prolonged, active use of immunosuppressive medications such as systemic steroids, or with a medical condition that requires systemic immunosuppression. 2. Active autoimmune disease that has required systemic treatment in the past 2 years. 3. Patients with a recognized immunodeficiency disease including cellular immunodeficiencies, hypogammaglobulinemia or dysgammaglobulinemia; patients who have acquired, hereditary, or congenital immunodeficiencies 4. Previous severe allergic reaction or hypersensitivity to a vaccine or to anti-PD-1 therapy or any of its components. 5. Requires anticoagulation that cannot be interrupted for biopsy and intratumoral injection. 6. Patient with an uncontrolled intercurrent illness. 7. Patient who has required a blood transfusion in the past 2 weeks. 8. Patient with active or chronic infection of HIV, HCV, or HBV. 9. The patient has received chemotherapy within 4 weeks prior to study drug administration. 10. Patients with a history of prior treatment with anti-PD-1/anti-PD-L1 agents. 11. The patient has received radiation to the planned injection site within 4 weeks prior to study drug administration. 12. The patient has received other investigational agents within 4 weeks prior to study drug administration. 13. Patients who have had surgery within 4 weeks prior to study drug administration, excluding minor procedures (dental work, skin biopsy, etc.). 14. Patients who have received any non-oncology live vaccine therapy used for prevention of infectious diseases within 4 weeks of study treatment. Examples include, but are not limited to, the following: measles, mumps, rubella, chicken pox, yellow fever, rabies, BCG, and typhoid vaccine. \*Note: Seasonal influenza vaccines for injection are generally killed virus vaccine and are allowed. However, intranasal influenza vaccines (e.g. Flu-Mist) are live-attenuated vaccines and are not allowed within 4 weeks of study treatment. 15. Pregnant women are excluded from this study because of the potential for teratogenic or abortifacient effects of this therapy. Because there is an unknown but potential risk for adverse events in nursing infants, breastfeeding should be discontinued if the mother is treated on study. 16. A history of current or recent invasive malignancy, unless disease free for a minimum of 3 years. Exceptions include basal cell or squamous cell carcinomas of the skin that have received potentially curative therapy. 17. The patient has known active central nervous system disease (CNS). For patients with treated brain metastases, they are eligible if follow-up brain imaging after central nervous system (CNS)-directed therapy shows no evidence of progression 18. Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial. 19. Inability to understand or unwillingness to sign an informed consent document