oAfter completion of enrollment on DL2 of Arm 1A, enrollment to Arm 1B will proceed if  out of 3 or 1 out of 6 participants in DL2 of Arm 1A experience a DLT. oIf 2 participants in a given dose level of Arm 1A or Arm 1B experience a DLT, accrual to that arm will be halted. There will be a 4-week DLT evaluation period for each dose level. There will be a 1-week delay between the first three participants treated on a given dose level. All other participants will be enrolled a minimum of six days apart on the phase I portion of the protocol except between the last participant in one dose level and the first participant in the next dose level in which case the DLT period of 4 weeks will be the minimum wait time. 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. Schema for Phase I 28 Abbreviated Title: Combo Immunotx in HPV OPSCC Version Date: 04.25.2023 Phase II: Newly diagnosed stage I (T1,T2 N1)/II/III HPV-positive oropharyngeal cancer and newly diagnosed stage II/III/IVA/IVB HPV-positive sinonasal squamous carcinoma: Evaluation of HPV vaccine alone (Arm 2A) as neoadjuvant or induction therapy in HPV- positive oropharyngeal cancer (20 participants), and HPV-SNSCC participants (2 participants). After completion of induction immunotherapy participants will be referred back to their home institution for definitive standard of care therapy.