Pilot Study of Induction Therapy Followed by Response-adaptive Treatment and Dynamic Changes in Circulating Tumor DNA in Locoregionally Advanced HPV Negative Head and Neck Squamous Cell Carcinoma

Inclusion Criteria: * Patients must have pathologically confirmed locally advanced, non-metastatic, human papillomavirus (HPV) negative head and neck squamous cell carcinoma of the oral cavity, oropharynx, hypopharynx, nasopharynx, larynx, or sinuses. * Stage III or IV disease based on American Joint Committee on Cancer (AJCC) staging 8th edition. * If a primary oropharyngeal squamous cell carcinoma is diagnosed, HPV must be ruled out by immunohistochemistry. * Availability of ≥10 unstained 5 micron slides. Patients who cannot fulfill this requirement will need to undergo a new biopsy prior to enrollment on study. * Patients must be at least 18 years of age. * Measurable disease (either primary site and/or nodal disease) by RECIST 1.1 criteria. * No previous radiation or chemotherapy for a head and neck cancer. * No complete surgical resection for a head and neck cancer within 8 weeks of enrollment (although lymph node biopsy including excision of an individual node with presence of residual nodal disease, or surgical biopsy/excision of the tumor with residual measurable disease is acceptable.) No surgical procedures or core-needle or excisional biopsies will occur after baseline scans are performed and measurable lesions are identified. Fine-needle aspiration can be performed (i.e., to confirm extent of baseline lymph node involvement) following discussion with PI if not performed on a target lesion. * Performance status 0-1 * Normal Organ Function * Leukocytes ≥ 3000/mm3 * Platelets ≥ 100,000/mm3 * Absolute neutrophil count ≥ 1,500 * Hemoglobin ≥ 9.0 gm/dL * Aspartate Aminotransferase (AST) ≤ 2.5x upper limit of normal * Alanine aminotransferase (ALT) ≤ 2.5x upper limit of normal * Alkaline phosphatase ≤ 2.5x upper limit of normal * Albumin \> 2.9 gm/dL * Total bilirubin ≤ 1.5 mg/dL * Creatinine clearance (CrCl) \> 45 mL/min, normal within 2 weeks prior to start of treatment (Of note, the standard Cockcroft and Gault formula must be used to calculate CrCl for enrollment or dosing) * Patients must sign a study-specific informed consent form prior to study entry. Patients should have the ability to understand and the willingness to sign a written informed consent document. * Women of childbearing potential must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of HCG) within 24 hours prior to the start of study drug. * Women must not be breastfeeding * Women of childbearing potential must agree to follow instructions for method(s) of contraception for the duration of treatment with study drug(s) plus 5 months after completing chemoradiation or receiving the last dose of chemoradiation, whichever occurs latest. * Men who are sexually active with women of childbearing potential must agree to follow instructions for method(s) of contraception for the duration of treatment with study drug(s) plus 5 months after completing chemoradiation or receiving the last dose of chemoradiation, whichever occurs latest. Exclusion Criteria: * Unequivocal demonstration of distant metastatic disease (M1 disease). * Unidentifiable primary site. * Intercurrent medical illnesses which would impair patient tolerance to therapy or limit survival. This includes but is not limited to ongoing or active infection, immunodeficiency, symptomatic congestive heart failure, pulmonary dysfunction, cardiomyopathy, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance. Patients with clinically stable and/or chronically managed medical illnesses that are not symptomatic and/or are not expected to impact treatment on protocol are still eligible (conditions to be reviewed by the PI to confirm eligibility). * Prior surgical therapy other than incisional/excisional biopsy or organ-sparing procedures such as debulking of airway-compromising tumors. Residual measurable tumor is required for enrollment as discussed above. * Patients receiving other investigational agents. * Diagnosis of immunodeficiency or is receiving systemic steroid therapy in excess of physiologic dose or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment. * Known history of active tuberculosis (Bacillus Tuberculosis infection). * Hypersensitivity to cetuximab or any other drug used in this protocol. * Prior systemic anti-cancer treatment within the last 8 weeks. * Has a known additional malignancy that is progressing or requires active treatment. Exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer or any tumors that are not likely to influence life expectancy in the subsequent 3 years without active treatment. * Has a history of HIV. * Has known active Hepatitis B or Hepatitis C. If eradicated, patient is eligible. * Has received a live vaccine within 28 days of planned start of study therapy.