University of Kansas Medical Center

All Patients: - Documentation of confirmed HPV 16+ cancer via genotype testing. - ≥ 1 measurable lesion by imaging for tumor response following RECIST - ECOG performance status of 0 to 1. - Prior curative radiation therapy and prior focal palliative completed per protocol-specified wash-out windows. - Screening laboratory values must meet protocol-specified criteria. - Able to provide tumor tissue following last treatment, unless otherwise agreed. Treatment Group E or Group F: - Documentation of confirmed head and neck squamous cell carcinoma. - Eligible to receive pembrolizumab, per standard of care and product label. - Group E: this group includes first line / 1L patients who have not yet received treatment in the metastatic/recurrent setting. - Group F: Tumor progression or recurrence on standard of care therapy, including ≥1 systemic therapy. Imaging Sub-Study (for specific participants at Memorial Sloan Kettering Cancer Center only): - Meeting requirements of inclusion criteria for Treatment Group 1 or Group 3. - At least 1 non-irradiated measurable lesion documented through imaging.

All patients: - Metastatic central nervous system disease, and/or carcinomatous meningitis. - Any serious or uncontrolled medical disorder that, in the opinion of the Investigator, may increase the risk associated with study participation / treatment administration. - Concurrent malignancy that is clinically significant or requires active intervention, unless protocol-defined criteria are met. - Active, known or suspected, autoimmune or inflammatory disorders requiring immunosuppressive therapy. - Has a life expectancy of less than 3 months. - Any toxicities attributed to systemic prior anticancer therapy o that have not resolved to Grade 1 or baseline prior to the first administration of study drug, unless protocol-defined criteria is met. - Not meeting the protocol-specified washout periods for prohibited medications. - Prior anaphylactic reaction to or known allergy or hypersensitivity to investigational product(s) or any of the excipients of the investigational product(s). - Positive hepatitis B surface antigen (HBsAg) or hepatitis C virus (HCV) antibody, indicating acute or chronic infection. - Known history of acquired immunodeficiency syndrome. For patients in Groups E or F and certain backfill cohorts: - History of severe hypersensitivity reaction to or other contraindication to receiving pembrolizumab. - History of/Presently having non-infectious pneumonitis requiring treatment. - Was discontinued due to a Grade 3 or higher immune-related AE (irAE) after receiving prior therapy with check point inhibitors. Imaging Sub-Study (for specific participants at Memorial Sloan Kettering Cancer Center only): - Having splenic disorders or prior splenectomy, and can compromise protocol objectives per Investigator and/or Sponsor. - Meeting requirements of exclusion criteria for Treatment Group 3