The purpose of this study is to evaluate the effects, good and/or bad, of treating participants with HPV-mediated oropharyngeal cancer, with less treatment, using the new staging system. The investigators believe this treatment will provide the same effectiveness as the usual treatment, but decrease the side effects. The radiation doses, chemotherapy doses, and the type of surgical approaches that will be used in this treatment protocol have all been previously investigated. Previous research suggests that this can be done safely, but there has not been a study done basing treatment on the new staging system.

Inclusion Criteria:

• Participants must have newly diagnosed, histologically, or cytologically confirmed HPV positive, squamous cell carcinoma of the base of tongue, tonsil, oropharyngeal cavity or unknown primary.
• Participants must have tumors staged using AJCC TNM 8th edition Staging for Head and Neck cancers.
• Participants must have an exam by a Head and Neck Oncologist within 6 weeks before registration.
• Participants must not have any evidence of distant metastatic disease.
• Participants with other active malignancies may be eligible, at the discretion of the investigator, as long as the treatment plan for the head and neck cancer outlined in this protocol can still be followed. The potential effect of the treatment and disease progress of the second active malignancy should also have minimal or no impact on the toxicities being monitored on this study.
• Participants must not have any uncontrolled intercurrent illnesses, psychiatric illnesses, psychosocial problems, or social situations that would limit the patient's compliance with the study or ability to successfully complete the study treatment safely.
• Participants with inconclusive pathology after biopsy; who are found to have HPV positive SCC following standard of care surgery are eligible to enroll.
• Participants who require additional surgery to complete staging with known HPV+ SCC are eligible to enroll.

Exclusion Criteria:

• Participants must not be receiving or planning to receive any other clinical trial therapy or intervention.
• Participants with an unknown primary tumor who are both HPV positive and EBV positive are NOT eligible for this protocol.

These additional evaluations must be performed on participants with T0 (unknown primary site) P16+ squamous cell carcinoma of the head and neck prior to registration.

• Flexible laryngoscope
• Ultrasound guided Fine-needle aspirate (FNA) of the known site of disease with the following analysis:
• Human papilloma virus (HPV); p16 Immuno-Histo-Chemical Staining. If negative, complete high risk HPV Fluorescence in-situ Hybridization (FISH).
• Epstein Barr Virus (EBV): Epstein Barr Virus Encoded RNA (EBER) in-situ Hybridization.
• Direct Laryngoscopy with directed biopsy of bilateral base of tongue, bilateral palatine tonsillectomy, and dental extraction, as needed.

If a participant is both HPV positive and EBV positive, he/she is not eligible.

Participants must have newly diagnosed, histologically, or cytologically confirmed HPV positive, squamous cell carcinoma of the base of tongue, tonsil, oropharyngeal cavity or unknown primary. Participants must have tumors staged using AJCC TNM 8th edition Staging for Head and Neck cancers.