Induction TPN Followed by Nivolumab With Radiation in Locoregionally Advanced Laryngeal and Hypopharyngeal Cancer

Inclusion Criteria: * Subject must have histologically or cytologically confirmed, resectable or unresectable, Stage III or Stage IV locoregionally advanced squamous cell carcinoma of the larynx or hypopharynx, as defined by 2017 American Joint Committee on Cancer (AJCC), 8th edition * Willing to provide tissue from diagnostic biopsy and blood samples before, during, and after treatment * Any smoking history is permitted * Patients must have HPV negative disease. Those patients with a supraglottic primary are required to undergo HPV testing with p16 immunohistochemistry and/or confirmatory HPV PCR or ISH testing to rule out oropharyngeal origin with laryngeal extension * Age 18 years or older * ECOG performance status ≤ 1 (Karnofsky ≥ 80%, see Appendix A) * Participant must have normal organ and marrow function as defined below within 21 days prior to study registration: * leukocytes ≥3,000/mcL * absolute neutrophil count ≥1,500/mcL * platelets ≥100,000/mcL * total bilirubin ≤2.0 g/dL * AST(SGOT)/ALT(SGPT) ≤2.5 × institutional upper limit of normal * creatinine within normal institutional limits OR * creatinine clearance ≥60 mL/min/1.73 m2 for participants with creatinine levels above institutional normal * Ability to understand and the willingness to sign a written informed consent document * Women of childbearing potential (WOCBP) must agree to use appropriate method(s) of contraception. WOCBP should plan to use an adequate method to avoid pregnancy for 5 months (30 days plus the time required for nivolumab to undergo five half-lives) after the last dose of investigational drug * 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 nivolumab * Women of childbearing potential (WOCBP)" is defined as any female who has experienced menarche and who has not undergone surgical sterilization (hysterectomy or bilateral oophorectomy) or who is not postmenopausal. Menopause is defined clinically as 12 months of amenorrhea in a woman over 45 in the absence of other biological or physiological causes. In addition, women under the age of 55 must have a documented serum follicle stimulating hormone (FSH) level less than 40 mIU/mL * Men who are sexually active with WOCBP must agree to use any contraceptive method with a failure rate of less than 1% per year. Men who are sexually active with WOCBP will be instructed to adhere to contraception for a period of 7 months after the last dose of investigational product. Women who are not of childbearing potential (ie, who are postmenopausal or surgically sterile as well as azoospermic men) do not require contraception Exclusion Criteria: * Existing severe autoimmune conditions (at the discretion of the treating physician). Patients with a history of Hashimoto thyroiditis who are stable on replacement hormone therapy are not excluded. Short-term corticosteroid dosing is permitted (i.e. dexamethasone for chemotherapy-induced nausea prevention during induction chemotherapy) as long as steroids are discontinued within 1 week (7 days) of receiving the first dose of nivolumab during the induction phase of treatment. * Subject who has had prior chemotherapy for head and neck cancer and/or radiotherapy to the head and neck. * Subject who has been treated with immunotherapy. This includes prior treatment with anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CTLA-4 antibody, or any other antibody or drug specifically targeting T-cell co-stimulation or immune checkpoint pathways. * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Known human immunodeficiency virus carrier or a diagnosis of immunodeficiency. Any positive test result for hepatitis B virus or hepatitis C virus indicating presence of virus, e.g., Hepatitis B surface antigen (HBsAg, Australia antigen) positive, or Hepatitis C antibody (anti-HCV) positive (except if HCV-RNA negative). * Known non-infectious pneumonitis or any history of interstitial lung disease. * 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, and low-risk prostate adenocarcinoma being managed with active surveillance. A history of another separate malignancy in remission without evidence of active disease in the last 5 years is permitted.