Study of Xevinapant With Radiation and Chemotherapy for Patients With Head and Neck Cancer

Inclusion Criteria: 1. Pathologically proven diagnosis of squamous cell carcinoma of the head and neck (HNSCC) of the oral cavity, oropharynx, larynx, hypopharynx, nasopharynx, or sinuses. * Patients with oropharynx cancer need p16 determination by immunohistochemistry (where positive is defined as greater than 70% strong nuclear or nuclear and cytoplasmic staining of tumor cells). * Oral cavity, larynx, hypopharynx, or p16-negative oropharynx cancer must be stages T1-2N1-3 or T3-4N0-3 (AJCC 8th edition). Sinus primary must be T4bN0-3 not amenable to surgical resection. * P16-positive oropharynx cancer patients, stages T1-2N1-3 or T3-4N0-3 (AJCC 8th edition staging). 2. The patient has unresected, measurable disease as defined by the presence of at least one measurable lesion per RECIST 1.1. 3. Age \>= 18 years of age 4. Patients must have a contraindication to cisplatin 5. Performance Status of 0-2 6. Adequate hematologic function * White Blood Cell Count (WBC) \>= 2000 cells/mm3 * Absolute neutrophil count (ANC) \>= 1,500 cells/mm3 * Platelets \>= 100,000 cells/mm3 * Hemoglobin \>= 9.0 g/dL 7. Adequate renal function was defined as follows: Creatinine clearance (CrCl) \> 30 mL/min 8. Adequate hepatic function * Total bilirubin \<= 1.5 x upper limit of normal (ULN) (except patients with Gilbert Syndrome who can have total bilirubin \< 3.0 mg/dL) * aspartate aminotransferase (AST) and alanine transaminase (ALT) \<= 2.5 x upper limit of normal (ULN) 9. For women of childbearing potential (e.g. uterus present and menstruating), a negative serum pregnancy test within 14 days prior to registration. 10. Willingness to agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) from time of joining the study until 6 months after completing chemotherapy treatment or 3 months after last dose of xevinapant, whichever is the latest. 11. Patients with a history of hepatitis B or C infection are eligible if they have an undetectable viral load. 12. Ability to understand and the willingness to sign a written informed consent document. 13. Availability of tumor tissue for research analysis. Patients who do not have adequate tissue available will need to undergo a new biopsy prior to enrollment on study. Exclusion Criteria: 1. Definitive clinical or radiologic evidence of distant (beyond cervical lymph node and neck tissue) metastatic disease. 2. Carcinoma of the neck of unknown primary site of origin 3. Prior systemic chemotherapy for the study cancer; note that prior chemotherapy for a different cancer is allowable if not within \< 3 years 4. Prior radiotherapy to the region of the study cancer that would result in overlap of radiation therapy fields; 5. Severe, active co-morbidity defined as follows: * History of bone marrow transplant and organ transplant, including allogeneic stem cell transplantation. * Unstable angina requiring hospitalization in the last 6 months. * New York Heart Association Functional Classification III/IV. * Myocardial infarction within the last 6 months. * Persistent Grade 3-4 electrolyte abnormalities that cannot be reversed despite as indicated by repeat testing. * Ongoing active infection associated with symptoms and/or requires antibiotic therapy at the time of initiation of treatment. 6. Pregnancy and nursing females, if applicable. 7. Receipt of live vaccinations within 28 days prior to study start. 8. Patients who are receiving any other investigational agents. 9. Patients with a "currently active" second malignancy other than non-melanoma skin cancers. Patients are not considered to have a "currently active" malignancy if they have completed therapy and are free of disease for ≥ 3 years. 10. History of allergic reactions attributed to compounds of similar chemical or biologic composition to xevinapant, carboplatin, or paclitaxel. 11. Patients taking prohibited medications and those requiring close monitoring.