Quarterback 2b - Sequential Therapy With Reduced Dose Chemoradiotherapy for HPV Oropharynx Cancer

Inclusion Criteria: Participants must meet the following criteria to be eligible to participate in the study. Patients may enroll in the study if they meet all of the entry criteria, were candidates for induction chemotherapy regardless of HPV status and have to start therapy for logistic reasons prior to p16 and HPV testing. They will enter the experimental post-Induction portion of the study if the surgical specimens or biopsies are proven to be HPV+ on PCR testing. Patients who are HPV negative will be taken off study and treated with SOC radiotherapy and surgery: * Participants must have histologically or cytologically confirmed squamous cell carcinoma of the oropharynx, hypopharynx, supraglottic larynx, nasal cavity, unknown primary, or nasopharynx that is p16 and HPV positive. Tissue from the primary site or lymph node must be available for biomarker studies and for PCR testing. IHC must be performed in a lab verified by the central laboratory or the slides must be available for review by the central laboratory and PCR must be done in the central laboratory prior to radiotherapy. HPVPCR must be performed and results available for reduced dose therapy after induction. * Patients who are on the Quarterback Trial when Quarterback 2 is activated and who have been randomized to radiotherapy arm will be asked to transfer to this trial and receive the Quarterback 2 defined radiotherapy. * Stage 3 or 4 disease without evidence of distant metastases. * At least one clinically evaluable or uni- or bi-dimensionally measurable lesion by RECIST 1.1 criteria. * Age ≥ 18 years. * No previous surgery, radiation therapy or chemotherapy for SSCHN (other than biopsy or tonsillectomy) is allowed at time of study entry. * ECOG performance status of 0 or 1. * No active alcohol addiction (as assessed by medical caregiver and defined as at least 6 months without activity). * Participants must have adequate bone marrow, hepatic and renal functions as defined below: * \- Hematology: * \- Neutrophil count ≥ 1.5 x 10\^9/l. * \- Platelet count ≥ 100 x 10\^9/l. * \- Hemoglobin ≥ 10g/dl. * \- Renal function ≥ 60 ml/min (actual or calculated by the Cockcroft-Gault method) as follows: CrCl (ml/min) = (140-age)(weight kg)/(mL/min) / 72 x serum creatinine (mg/dL) * \- N.B. For females, use 85% of calculated CrCl value. Or a Creatinine ≤ the upper limits of normal * \- Hepatic: * \- Total Bilirubin ≤ institutional upper level of normal (ULN) * \- AST or ALT and Alkaline Phosphatase must be within the range allowing for eligibility * Women of childbearing potential must have a negative pregnancy test within 7 days of starting treatment. * Ability to understand and the willingness to sign a written informed consent document. * Patients with Gilbert's Disease and absent hepatic pathology by history and clinical assessment may be treated on study with bilirubin \> the ULN for the institution if other liver functions studies are within the normal range Exclusion Criteria: * Pregnant or breast feeding women, or women and men of childbearing potential not willing to use adequate contraception while on treatment and for at least 3 months thereafter. * Previous or current malignancies at other sites, with the exception of adequately treated in situ carcinoma of the cervix, basal or squamous cell carcinoma of the skin, thyroid cancer, or other cancer curatively treated by surgery and with no current evidence of disease for at least 5 years. * Symptomatic peripheral neuropathy grade \> 2 by NCI Common Terminology Criteria (NCI-CTC) version 4. * Symptomatic altered hearing \> grade 2 by NCI-CTCv4 criteria.These patients can be entered by substituting carboplatin for cisplatin with an AUC of 6.0 * Other serious illnesses or medical conditions including but not limited to: * \- Unstable cardiac disease despite treatment, myocardial infarction within 6 months prior to study entry * \- History of significant neurologic or psychiatric disorders including dementia or seizures * \- Active clinically significant uncontrolled infection * \- Active peptic ulcer disease defined as unhealed or clinically active * \- Hypercalcemia * \- Active drug addiction including alcohol, cocaine or intravenous drug use defined as occurring within the 6 months preceding diagnosis * \- Chronic Obstructive Pulmonary Disease, defined as being associated with a hospitalization for pneumonia or respiratory decompensation within 12 months of diagnosis. This does not include obstruction from tumor * \- Autoimmune disease requiring therapy, prior organ transplant, or HIV infection * \- Interstitial lung disease * \- Hepatitis C by history, and confirmed by serology * Patients that have experienced an involuntary weight loss of more than 25% of their body weight in the 2 months preceding study entry. * Concurrent treatment with any other anticancer therapy. * Participation in an investigational therapeutic drug trial within 30 days of study entry. * Active smoking or a cumulative pack year history of \> 20 pack years, active smoking is (Defined as ≥ 1 cigarette per day) within the last 5 years.