At outside institutions, standard of care treatment will be performed and chosen solely by outside providers. NCI investigators will have no role in treatments received at outside institutions. Schema for Phase II Although positive HPV testing will not be required for the phase I or II portion of the protocol prior to enrolling, HPV testing will be offered as an exploratory endpoint and participants testing negative for HPV after enrolling or whose HPV status cannot be confirmed may be replaced with other participants for the primary efficacy analysis. Participants testing negative for HPV after enrolling or whose HPV status cannot be confirmed may continue to receive treatment on study. 3.1.1 Dose Limiting Toxicity (for first 3-6 participants enrolled on Arms 1A and 1B; phase I part of the study): Dose-limiting toxicity (DLT) will be defined as any one of the following adverse events, possibly attributable to study drugs, that occur within 28 days of the HPV vaccine monotherapy or 28 days of starting the HPV vaccine + M7824 combination therapy: Any Grade 3 or higher bleeding episode requiring blood transfusion(s). Any Grade 4 or higher adverse drug reactions (ADRs) as defined by CTCAE v5.0 and assessed as possibly related to any agent by the Investigator, except for laboratory values that are asymptomatic or resolve to Grade ≤ 1 or baseline grade within 7 days without medical intervention. Any Grade 3 ADRs possibly attributed to any agent except for any of the following: 29 Abbreviated Title: Combo Immunotx in HPV OPSCC Version Date: 04.25.2023 oGrade 3 flu-like symptoms or fever, as well as associated symptoms of fatigue, headaches, nausea, emesis which can be controlled with conservative medical management. oTumor flare phenomenon defined as local pain, irritation, or rash localized at sites of known or suspected tumor. oGrade 3 Hgb decrease (< 8.0 g/dL) that is clinically manageable with blood transfusions or erythroid growth factor use does not require treatment discontinuation. oGrade 3 laboratory values that are asymptomatic or resolve to Grade ≤ 1 or baseline grade within 7 days without medical intervention. oKeratoacanthoma and squamous cell carcinoma of the skin. oAny endocrinopathy that can be medically managed with hormone replacement oAny grade 3 adverse drug reaction which can be medically managed with minimal risk to the participants (e.g., placement of a pleural catheter for recurrent inflammatory pleural effusions) and resolves to at least grade one or baseline grade within 72 hours. Where clinically appropriate subjects enrolled on Arm 1 will receive one year of treatment during which subjects will be followed with surveillance scans using CT/MRI (as appropriate) every 6- 12 weeks. On a case by case basis treatment beyond a year is allowed per investigator discretion. Subjects with evidence of disease progression after completing a year of treatment will be allowed retreatment. Patients might be taken off treatment for disease progression prior to completing one year of treatment, but where clinically appropriate, treatment beyond radiographic progression is allowed if in the opinion of the investigator the subject is benefiting from treatment. Subjects will be taken off treatment if unacceptable toxicity occurs and is attributed to all therapeutic agents. If a single agent is tolerated that agent may be continued. 3.2 DRUG A DMINISTRATION General Rule For participants enrolled on the phase I portion of the protocol a window of +/- 14 days for a scheduled treatment is allowed in the event of scheduling issues (i.e., holiday, bad weather or other scheduling issues). For participants enrolled on the phase II portion of the protocol a window of +/- 7 days for a scheduled treatment is allowed in the event of scheduling issues (i.e., holiday, bad weather or other scheduling issues). The minimum time between administrations of a similar agent is 11 days. Where feasible PRGN-2009 should be administered first, followed by M7824 (when given). 3.2.1 PRGN-2009 On the phase I portion of the protocol PRGN-2009 will be administered on D1, D15, D29 followed by booster vaccines every 4 weeks for up to a year. The dose level given as booster will be the same dose participants will be receiving for D1, D15 and D29. On the phase II portion of the protocol PRGN-2009 will be administered on just D1 and D15. 3.2.1.1 Refer to Sections 14.1.4 Pharmacy Preparation and 14.1.5 Vaccine Preparation 3.2.1.2 Administration Procedures Injection Volume – The injection volume for both doses is 1.0 ml. 30 Abbreviated Title: Combo Immunotx in HPV OPSCC Version Date: 04.25.2023 Injection Route – The route of injection is by subcutaneous injection using a 1.0 ml syringe. Follow your standard institutional clinical procedures for preparation of the subject’s injection site, subcutaneous injection and post-injection bandaging of the injection site. PRGN-2009 is a non- replicating, non-integrating adenoviral vector. Since the parental adenovirus is classified as biosafety level 2 (BSL2), PRGN-2009 should be handled as BSL2 material for disposal of all materials that were used in the dose administration. Spills of PRGN-2009 should be decontaminated using a solution of 10% bleach. 3.2.2 M7824 Subjects enrolled to Arm 1B will receive M7824 via IV infusion over 1 hour (-10 minutes / +20 minutes, that is, over 50 to 80 minutes) once every 2 weeks for up to a year (Arm 1B). M7824 will be administered as a "flat" dose of 1,200 mg independent of body weight. M7824 is administered as an intravenous infusion with a mandatory 0.2 micron in-line filter. Infusion of M7824 can be administered through a PIV or CVAD or port with titanium as the main material. Current experience revealed that IRRs to M7824 occur seldomly and are generally mild to moderate in severity. Therefore, administration of a premedication is generally not required. In order to mitigate potential infusion-related reactions, premedication with an antihistamine and with acetaminophen (for example, 25-50 mg diphenhydramine and 500-650 mg acetaminophen) within approximately 30 to 60 minutes prior to dosing of M7824 is optional and at the discretion of the Investigator. Management of symptoms should follow the guidelines shown in Table 2. 3.2.2.1 Immediate Hypersensitivity Reaction Hypersensitivity reactions may require immediate intensive care. M7824 should be administered in a setting that allows for immediate access to an intensive care unit or equivalent environment and administration of therapy for anaphylaxis, such as the ability to implement immediate resuscitation measures. Steroids (dexamethasone 10 mg), epinephrine (1:1,000 dilution), allergy medications (IV antihistamines), bronchodilators, or equivalents, and oxygen should be available for immediate access. A complete guideline for the emergency treatment of anaphylactic reactions according to the Working Group of the Resuscitation Council United Kingdom and can be found at https://www.resus.org.uk/pages/reaction.pdf. 3.2.2.2 Flu-Like Symptoms Treatment is based on clinical assessment and at the discretion of the Investigator. For prophylaxis of flu like symptoms, a nonsteroidal anti-inflammatory drug (NSAID), e.g., ibuprofen 400 mg or comparable NSAID dose, may be administered 2 hours before and 8 hours after the start of each IV infusion. 3.3 DOSE MODIFICATIONS 3.3.1 Discontinuation Phase 1 and Phase 2: 31 Abbreviated Title: Combo Immunotx in HPV OPSCC Version Date: 04.25.2023 Treatment with individual agents (PRGN-2009 alone or in combination with M7824) will be discontinued in participants experiencing specific adverse events; subjects will however still remain on study for follow up of survival. Treatment discontinuation will occur in any participant experiencing a DLT-defining toxicity and in the case of: Any Grade 4 or higher adverse drug reactions (ADRs) as defined by CTCAE v5.0 and assessed as possibly related to that agent by the Investigator, except for any of the following: oLaboratory values that are asymptomatic or resolve to Grade ≤ 1 or baseline grade within 7 days without medical intervention. oAny endocrinopathy that can be medically managed with hormone replacement. Any Grade 3 ADRs possibly attributed to that agent except for any of the following: oGrade 3 flu-like symptoms or fever, as well as associated symptoms of fatigue, headaches, nausea, emesis which can be controlled with conservative medical management. oTumor flare phenomenon defined as local pain, irritation, or rash localized at sites of known or suspected tumor. oGrade 3 Hgb decrease (< 8.0 g/dL) that is clinically manageable with blood transfusions or erythroid growth factor use. oGrade 3 laboratory values that are asymptomatic or resolve to Grade ≤ 1 or baseline grade within 7 days with medical management. oKeratoacanthoma and squamous cell carcinoma of the skin. oAny endocrinopathy that can be medically managed with hormone replacement. oAny other grade 3 adverse drug reaction that resolves to grade <1 or baseline grade within 72 hours. 3.3.2 Dose Delay Individual agents should be withheld for any Grade 2 or 3 ADR possibly attributed to that agent until resolution to Grade ≤ 1 unless the ADR in the opinion of the investigator is not clinically relevant or can be medically managed with minimal risk to the participant. Should a clinically relevant grade 2 or 3 ADR persist for more than 4 weeks, consideration should be given to discontinuing treatment with that individual agent at the discretion of the investigator. For non-medical logistical reasons, unrelated acute illnesses, or palliative radiation, scheduled assessments and dosing can be delayed up to 2 months. Where at all possible, dosing should be restarted to keep in line with the original treatment schedule. 3.3.3 Study Accrual Halting Rules Accrual will be halted if: Phase 1 and Phase 2: oThere is an occurrence of any death (other than death related to progressive disease or accidental death) that occurs within 30 days of administration of study agents (PRGN-2009 and M7824) for both Phase 1 and Phase 2. Phase 2 only: oThere is a delay in initiation of definitive standard of care therapy of 4 weeks or more beyond the planned start date due to treatment-related toxicities from HPV vaccine in two participants. 32 Abbreviated Title: Combo Immunotx in HPV OPSCC Version Date: 04.25.2023 oThere is occurrence of treatment-related ADRs from HPV vaccine of either Grade 4 (except for laboratory values that are asymptomatic or resolve to Grade ≤1 or baseline within 7 days) or of Grade 3 not resolving to Grade ≤1 or baseline within 7 days in two participants. The IRB and the sponsor will be notified if one of the study accrual halting rules has been reached.