A Phase 1/2 Study in Patients With HPV16+ Recurrent/Metastatic Head and Neck Squamous Cell Carcinoma and Other Cancers

Inclusion Criteria 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. Exclusion Criteria: 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