Individuals who do not meet the criteria for participation in this trial (screen failure) because of a transient lab abnormality may be rescreened. 2.3.2 Treatment Assignment Procedures 2.3.2.1 Cohorts Number Name Description 1 Cohort 1 Subjects with advanced or metastatic HPV associated malignancies (Phase I) 2 Cohort 2 Subjects with newly diagnosed p16+ oropharyngeal cancer (Phase II): Arm 2A: Stage I (T1,T2 N1)/II/III Arm 2B: Stage II/III Note: Closed, Will Not Enroll 3 Cohort 3 Subjects with newly diagnosed stage II/III/IVA/IVB HPV+ sinonasal squamous cell cancer (Phase II) 25 Abbreviated Title: Combo Immunotx in HPV OPSCC Version Date: 04.25.2023 2.3.2.2 Arms Number Name Description 1 Arm 1A HPV vaccine at 1x1011 Viral Particles (VP) (DL1) and at 5x1011 VP (DL2) Note: Closed, Enrollment Completed 2 Arm 1B HPV vaccine at RP2D plus M7824 at 1200 mg 3 Arm 2A HPV vaccine at RP2D given as neoadjuvant or induction therapy 4 Arm 2B HPV vaccine at RP2D plus M7824 at 1200 mg given as neoadjuvant or induction therapy Note: Closed, Will Not Enroll 2.3.2.3 Arm Assignment Participants in Cohort 1 will be sequentially assigned to Arm 1A, to determine RP2D of PRGN- 2009, and then Arm 1B, evaluating the combination of RP2D of PRGN plus M7824. Participants will be enrolled to these arms based upon a 3+3 dose escalation schema. In addition, Arm 1B will be expanded to a total of 10 evaluable participants to gauge the preliminary efficacy of the combination of PRGN-2009 and M7824 in participants with advanced disease. Once the RP2D of HPV vaccine has been determined, p16+ oropharyngeal cancer participants in Cohort 2 and HPV-SNSCC participants in Cohort 3 will be assigned to Arm 2A (20 evaluable participants for Cohort 2, up to 2 for Cohort 3). 2.4 BASELINE EVALUATION All subjects are required to complete baseline evaluations within two weeks (four weeks for Phase II imaging) prior to the first dose of the study drug (any screening evaluation done within this time period can also serve for the baseline evaluation unless otherwise indicated): Physical exam including weight, ECOG performance status and vital signs. Skin assessment. Medical history (Concomitant Medications and Baseline Signs and Symptoms evaluation). Imaging for Phase I*: CT of chest, abdomen and pelvis or MRI, if clinically indicated. A brain CT scan in participants with known CNS disease as described in Section 2.1.2.3/ MRI scan if clinically indicated. Imaging for Phase II*: 26 Abbreviated Title: Combo Immunotx in HPV OPSCC Version Date: 04.25.2023 CT of the neck† and chest+, or MRI, if clinically indicated, for participants with oropharyngeal cancer. CT of skull†, neck† and chest+, or MRI, if clinically indicated, for participants with sinonasal SCC. *Imaging for baseline should be within 2 weeks (for Phase I) or 4 weeks (for Phase II) prior to the first dose of study drug and is not required if available within the baseline timeframe. Imaging performed at outside facilities within the timeframe may also be used for baseline. +Imaging of chest is not required if a PET/CT is available within the baseline timeframe. †The CT component of a PET/CT obtained within the baseline timeframe may be used as CT of the neck ± skull per PI discretion. Urine or serum pregnancy test (β-HCG) for females of childbearing-potential and women < 12 months since the onset of menopause (within 5 days prior to study therapy). Acute care panel (Na+, K+, Cl-, total CO2, creatinine, glucose, blood urea nitrogen). Hepatic panel (AST/GOT, ALT/GPT, total bilirubin, direct bilirubin). Mineral panel (albumin, calcium total, magnesium total, phosphorus). Thyroid tests (TSH and reflex free T3 & T4), lipase, amylase, C-Reactive Protein (CRP). Hematology: CBC with differential. Coagulation panel: PT, INR, and PTT. HLA typing (any time prior to study treatment initiation - may be deferred if it has been previously performed at the NIH). (For Phase II only) Urinalysis. For correlative studies: Blood and tissue sample will be collected. Please refer to Section 5.1 for details regarding samples to be collected and refer to the Study Calendar for collection timepoints. Creatinine phosphokinase (CPK). 27 Abbreviated Title: Combo Immunotx in HPV OPSCC Version Date: 04.25.2023 3 STUDY IMPLEMENTATION 3.1 STUDY DESIGN Phase I: Recurrent/metastatic HPV associated cancer A 3+3 dose escalation design will be used which will evaluate PRGN-2009 (HPV vaccine) at two dose levels (1x1011 and 5x1011 VP) given as monotherapy followed by an evaluation of the RP2D dose of PRGN-2009 in combination with 1200 mg (RP2D) of M7824. Dose escalation will follow the rules as outlined: oAfter completion of enrollment on DL1 of Arm 1A, enrollment to DL2 of Arm 1A will proceed if 0 out of 3 or 1 out of 6 participants in DL1 of Arm 1A experience a DLT.