For this reason and because M7824 and PRGN-2009 used in this trial are possibly teratogenic, women of child-bearing potential and men must agree to use highly effective contraception (hormonal or barrier method of birth control; 21 Abbreviated Title: Combo Immunotx in HPV OPSCC Version Date: 04.25.2023 abstinence) prior to study entry and up to 2 months following the last dose of M7824 study treatment. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. 2.1.1.10 Participants serologically positive for HIV, Hep B, Hep C are eligible as long as the viral loads are undetectable by quantitative PCR. HIV positive participants must have CD4 count ≥ 200 cells per cubic millimeter at enrollment, be on stable antiretroviral therapy for at least 4 weeks and have no reported opportunistic infections or Castleman’s disease within 12 months prior to enrollment. 2.1.2 Exclusion Criteria 2.1.2.1 Participants with prior investigational drug, live vaccine, chemotherapy, immunotherapy or any prior radiotherapy (except for palliative bone directed therapy) within the past 28 days prior to the first drug administration except if the investigator has assessed that all residual treatment-related toxicities have resolved or are minimal and feel the participant is otherwise suitable for enrollment. Participants may continue adjuvant hormonal therapy in the setting of a definitively treated cancer (e.g., breast). 2.1.2.2 Major surgery within 28 days prior to the first drug administration (minimally invasive procedures such as diagnostic biopsies are permitted). 2.1.2.3 Known active brain or central nervous system metastasis (less than a month out from definitive radiotherapy or surgery), seizures requiring anticonvulsant treatment (<3 months) or clinically significant cerebrovascular accident (<3 months). In order to be eligible participants must have repeated CNS imaging at least a month after definitive treatment showing stable CNS disease. Participants with evidence of intratumoral or peritumoral hemorrhage on baseline imaging are also excluded unless the hemorrhage is grade ≤ 1 and has been shown to be stable on two consecutive imaging scans. 2.1.2.4 Pregnant women are excluded from this study because M7824 and PRGN-2009 vaccine have not been tested in pregnant women and there is potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with these immunotherapies, breastfeeding should be discontinued if the mother is treated on this protocol. 2.1.2.5 Only for Phase I, Arm 1B: Active autoimmune disease that might deteriorate when receiving an immunostimulatory agent with exception of: Diabetes type I, eczema, vitiligo, alopecia, psoriasis, hypo- or hyperthyroid disease or other mild autoimmune disorders not requiring immunosuppressive treatment; Administration of steroids for other conditions through a route known to result in a minimal systemic exposure (topical, intranasal, intro-ocular, or inhalation) is acceptable; Subjects on systemic intravenous or oral corticosteroid therapy with the exception of physiologic doses of corticosteroids (≤ the equivalent of prednisone 10 mg/day) or other immunosuppressors such as azathioprine or cyclosporin A are excluded on the basis of potential immune suppression. For these subjects these excluded treatments must be discontinued at least 1 weeks prior to enrollment for recent short course use (≤ 14 days) or discontinued at least 4 weeks prior to enrollment for long term use (> 22 Abbreviated Title: Combo Immunotx in HPV OPSCC Version Date: 04.25.2023 14 days). In addition, the use of corticosteroids as premedication for contrast-enhanced studies is allowed prior to enrollment and on study. 2.1.2.6 Only for Phase I: Subjects with a history of serious intercurrent chronic or acute illness, such as cardiac or pulmonary disease, hepatic disease, bleeding diathesis or recent (within 3 months) clinically significant bleeding events, known left ventricular ejection fraction <50% (confirmation of EF > 50% is not required for eligibility), history of myocarditis, or recent myocardial infarction (within 6 months), or other illness considered by the Investigator as high risk for M7824 drug treatment. 2.1.2.7 Only for Phase I: Subjects refusing to accept blood products as medically indicated. 2.1.2.8 History of second malignancy within 3 years of enrollment except for the following: adequately treated localized skin cancer, cervical carcinoma in situ, superficial bladder cancer, other localized malignancy which has been adequately treated or malignancy which does not require active systemic treatment (e.g., low risk CLL). For participants enrolled on the phase I portion of the protocol a second HPV driven malignancy is allowed. 2.1.2.9 Only for Phase I, Arm 1B: Subjects with a known severe hypersensitivity reaction to monoclonal antibodies or its excipients (grade >/= 3 NCI-CTCAE v5) will be evaluated by the allergy/immunology team prior to enrollment. 2.1.2.10 Prior allogenic tissue/solid organ transplant. 2.1.2.11 For participants who may receive M7824: previous life-threatening side effects resulting from prior checkpoint inhibitor therapy. 2.1.2.12 Participants with pulse oximetry < 92% on room air at screening. 2.1.2.13 Participants unable to provide informed consent. 2.1.2.14 Participants whose inclusion in the trial would in the judgement of the PI lead to time from diagnosis to initiation of curative treatment of >70 days (Arm 2A only). 2.1.3 Recruitment Strategies This protocol may be abstracted into a plain language announcement posted on NIH websites and on NIH social media platforms. This study will be listed on www.clinicaltrials.gov. This study may be advertised at national conferences including AACR and ASCO and may also be shared with the HPV and Anal Cancer Foundation who may advertise it further. Recruitment flyers may be used to advertise this study in the future after IRB approval. Participants for the Phase I portion of the study will be recruited from the current participant population at NIH. participants with HPV related cancers are currently being treated on another trial through LTIB, CCR, NIH, where 2-3 participants per month are being screening and enrolled. Some of these participants come from established community networks, some of these participants are self-referrals, and some of these participants are referred by another group (Dr. Norberg’s group, Experimental Transplantation and Immunology Branch, CCR, NIH) who also have a large referral base for HPV related cancers. Participants on the phase II portion of the study will be recruited from locoregional hospital including the Johns Hopkin’s community network of which Clint Allen, MD, an AI on this protocol, is also a part. 23 Abbreviated Title: Combo Immunotx in HPV OPSCC Version Date: 04.25.2023 2.2 SCREENING EVALUATION 2.2.1 Screening activities performed prior to obtaining informed consent Minimal risk activities that may be performed before the subject has signed a consent include the following: Email, written, in person or telephone communications with prospective subjects. Review of existing medical records to include H&P, laboratory studies, etc.