The phase II portion of this study would take advantage of this opportunity and offer the participant the chance to benefit from immunotherapy. Note: In September of 2021 we received a report by EMD Serono, the manufacturer of M7824, that three randomized clinical trials (two in non-small cell lung cancer and one in biliary tract cancer) had been terminated due to futility and the suggestion of increased toxicity in some subjects, or increased progression in a subset of subjects. This was reported to the Sponsor and the IRB and following review of submitted data it was decided to allow Phase I to proceed and Phase II Arm 2A (vaccine only) but to close Arm 2B (vaccine plus bintrafusp alfa) before enrollment started. The Phase II portion of this study will only consist of only Arm 2A PRGN-2009 alone. Studies that were to be conducted under Arm 2B will be removed from the rest of the protocol; however, will remain here (and in Section 2.3.2) for background and informational purposes. 1.2.10 Rationale summary Clinical outcomes for recurrent/metastatic HPV-positive malignancy and newly diagnosed stage II/III p16-positive OPSCC are poor, and while they are better for I (T1,2 N1) p16- positive OPSCC de-intensification is needed to reduce long-term toxicity. Participants with advanced p16-positive OPSCC have tumors infiltrated with exhausted and dysfunctional HPV antigen-specific T cells. Treatment with a vaccine targeting HPV oncogenes to induce antigen-specific immunity (PRGN-2009) combined with immune checkpoint blockade to fully activate new and existing antigen-specific T cells (M7824) is a rational combination treatment strategy. Investigators at the NIH Clinical Center have significant clinical experience with M7824. 19 Abbreviated Title: Combo Immunotx in HPV OPSCC Version Date: 04.25.2023 1200 mg flat dose of M7824 has been chosen based on a phase I dose escalation trial of M7824 in solid tumors done at the NCI and PK/ PD data from that trial (NCT02517398). DL1 and DL2 of PRGN-2009 has been chosen based on the dose used for other adenovirus vaccines. The phase I portion of the study will offer participants with immune checkpoint refractory recurrent/metastatic HPV-positive malignancy a chance to benefit from combination PRGN-2009 and M7824 treatment. The phase II portion of the study will offer participants the opportunity to benefit from immunotherapy during a period of time when they are normally scheduling and awaiting definitive therapy for their newly diagnosed HPV-positive OPSCC. Pre-treatment and post-treatment tumor biopsies before definitive therapy can provide tissue for studies aimed at interrogating the effects of single agent or combination immuno- oncologic treatments on the tumor microenvironment and correlating those effects with clinical activity. 1.2.11 Rationale and background for performing immune assays Multiple immune assays have been developed in the LTIB to better define the mechanism(s) involved in the use of specific novel agents, as monotherapy or in combination therapies, both for preclinical and clinical studies. In addition to analyses of biopsies, analyses of the peripheral immunome can provide valuable information where multiple samples can be analyzed over the course of a given therapy vs. pre-therapy. The LTIB has now developed and employed (45-48) a flow cytometry‒based assay that can analyze 123 immune cell subsets in human PBMC from one vial of processed PBMC (approximately 107 cells). This assay will be used in this clinical trial to detect multiple (n=32) subsets of CD4+ T cells, CD8+ T cells (n=29), Tregs (n=7), B cells (n=5), NK (n=20), NKT (n=4), DC (n=10), and MDSC (n=16) to better understand the role of each agent. We also plan to evaluate changes in TCR clonal diversity both in biopsies and the periphery. One example of where these assays have been employed involves an ongoing first-in-human trial of the NHS-IL12 tumor-targeting immunocytokine (NCT01417546). TCR diversity increased 6- 14‒fold in biopsies of patients with a high or intermediate IFN-γ response but were unchanged or decreased with a low IFN-γ response. These findings also correlated with TIL in biopsies. We are also currently employing NanoString analyses to identify a gene signature in biopsies and PBMC, pre- and post-treatment. The infiltration of p16-positive HNSCC with tumor infiltrating lymphocytes (TIL) tends to be greater than that observed in p16-negative HNSCC (49), possibly related to the presence of strong viral antigens. Supporting that these TIL are active and possess anti-tumor function, greater numbers of TIL present within p16-postive HNSCCs is positively correlated with increased survival after standard anti-cancer treatment and associated with an increased type I immune profile within the tumor ( 20). A meta-analysis of all published papers exploring TIL infiltration into p16-positive HNSCC demonstrated a strong, significant, positive correlation (50). Thus, changes in TIL infiltration into p16-positive HNSCCs after immunotherapy will be used for the primary outcome of the phase II portion of this study. In addition, the GMB will conduct multiplexed, multispectral imaging of FFPE tissue to evaluate multiple immune parameters within the TME before and after treatment in patients with available tissue. 20 Abbreviated Title: Combo Immunotx in HPV OPSCC Version Date: 04.25.2023 2 ELIGIBILITY ASSESSMENT AND ENROLLMENT 2.1 ELIGIBILITY CRITERIA 2.1.1 Inclusion Criteria 2.1.1.1 Subjects with cytologically or histologically confirmed locally advanced not amenable to potentially curative local therapies or metastatic HPV associated malignancies (Phase I only): Cervical cancers; p16+ Oropharyngeal cancers; Anal cancers; Vulvar, vaginal, penile, and squamous cell rectal cancers; Other locally advanced or metastatic solid tumors (e.g., lung, esophagus) that are known HPV+. 2.1.1.2 Subjects with cytologically or histologically confirmed newly diagnosed stage I (T1,2 N1), II or III p16-positive oropharyngeal squamous cell carcinoma planned for definitive therapy or with newly diagnosed stage II or III or IVA or IVB HPV-positive sinonasal squamous carcinoma (HPV-SNSCC) eligible for primary surgery (Phase II only). 2.1.1.3 Subjects must have measurable disease, per RECIST 1.1. See Section 6.3 for the evaluation of measurable disease (Phase 1 only). 2.1.1.4 Phase I only: Participants must have received one prior line of systemic chemotherapy in the recurrent/metastatic setting as well as checkpoint blockade therapy in tumors with FDA approval (head and neck squamous cell cancer and PDL1+ cervical cancer). Exceptions to this include participants not eligible to receive standard therapy.