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