15. Only for p16+ oropharyngeal cancer patients: Collection of saliva by mouth rinse and gargle with 15- 20 mL 0.9% NaCl for 30 seconds and spitting into the collection tube. Where possible, saliva samples will be analyzed for HPV DNA detection and quantification. 16. Skin assessment must be performed at baseline and at least every 6 weeks starting on week 5 during treatment and at the end of treatment or at the 28 (±7 days) day safety follow-up (if not performed in the previous 6 weeks). 44 Abbreviated Title: Combo Immunotx in HPV OPSCC Version Date: 04.25.2023 17. HLA A, B, C and DR, DQ and NGS A, B, C and DR, DQ, at any time prior to treatment start. Patients who have had HLA typing previously performed at NIH do not require retesting. 18. Preferably scheduled for Week 5, with Week 4 an option to not interfere with activities required for arrangements for definitive treatment. An earlier timepoint may also be used to avoid interfering with definitive treatment, but should be at least a day after the second vaccination. 19. Upon completion of induction or neoadjuvant immunotherapy participants on the phase II portion of the protocol will be taken off treatment and referred back to their home institutions for definitive standard of care therapy and follow up will be performed per superscript # 6 above. 45 Abbreviated Title: Combo Immunotx in HPV OPSCC Version Date: 04.25.2023 3.5 COST AND COMPENSATION 3.5.1 Costs NIH does not bill health insurance companies or participants for any research or related clinical care that participants receive at the NIH Clinical Center. If some tests and procedures are performed outside the NIH Clinical Center, participants may have to pay for these costs if they are not covered by an insurance company. Medicines that are not part of the study treatment will not be provided or paid for by the NIH Clinical Center. 3.5.2 Compensation Subjects will not receive compensation for participation in this study. 3.5.3 Reimbursement The NCI will cover the costs of some expenses associated with protocol participation. Some of these costs may be paid directly by the NIH and some may be reimbursed to the participant/guardian as appropriate. The amount and form of these payments are determined by the NCI Travel and Lodging Reimbursement Policy. 3.6 CRITERIA FOR REMOVAL FROM PROTOCOL THERAPY AND OFF STUDY C RITERIA Regardless of reason for removal from study therapy, participants will be asked to have a 28 day follow up safety visit. Participants who are unable or unwilling to return for this visit will be asked to review any safety concerns by phone within this time period. 3.6.1 Criteria for Removal from Protocol Therapy Completion of protocol therapy. Clinical or radiographic progression of disease except when the investigator feels the subject is still benefiting from treatment. (It is generally preferable for participants to remain on treatment past initial radiographic progression in case there is pseudo - progression, except when the investigator feels that the clinical picture warrants changing therapy at initial progression). Unacceptable toxicity possibly attributed to all active therapies (see Section 3.3). Participant requests to be withdrawn from active therapy. Start of another systemic anticancer treatment or participation in another investigational therapeutic trial (except for standard of care therapy for phase II participants). For participants enrolled in the phase I portion of the protocol, focal palliative radiotherapy, ablation, or surgery to a site of disease will not necessitate removal from protocol therapy. Investigator discretion. Positive pregnancy test. Intercurrent illness that prevents further administration of treatment, in the judgement of the investigator. 46 Abbreviated Title: Combo Immunotx in HPV OPSCC Version Date: 04.25.2023 3.6.2 Off-Study Criteria Failure to maintain eligibility criteria prior to starting treatment. Screen failure.