A Study of Cemiplimab With Chemotherapy and Immunotherapy in People With Head and Neck Cancer

Inclusion Criteria: * Pathologically (histologically or cytologically) proven diagnosis of squamous cell carcinoma of the head and neck that has arisen from the oral cavity, oropharynx, nasal cavity, paranasal sinuses, larynx, or hypopharynx * Clinical stage T1, N2-3; T2, N1-3, T3/T4a, Any N (AJCC, 8th ed.) without evidence of distant metastasis (M0) based on PET/CT or CT chest, abdomen, and pelvis, for which standard-of-care treatment would entail surgical resection with adjuvant radiation +/- chemotherapy. ° Patients with recurrent and multiple primary head and neck cancers that are surgically resectable are eligible if the patient did not receive prior radiation or systemic therapy. * Disease must be amenable to surgical resection. * The patient must be a surgical candidate. 1. Hemoglobin \> 9.0 g/dL 2. Absolute neutrophil count (ANC) \>1.5 x 10\^9/L 3. Platelet count \>100 x 10\^9/L 4. Serum creatinine \<1.5 upper limit of normal (ULN) or estimated creatinine clearance (CrCl) \>30 mL/min 5. Adequate hepatic function: * Total bilirubin \<1.5 x upper limit of normal ULN) * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) both \< 3 x ULN * Alkaline phosphatase (ALP) \<2.5 x ULN Note: For patients with Gilbert syndrome, total bilirubin \<3x ULN. Upper central must be documented appropriately as past medical history. * Men and woman \>18 years old * Eastern cooperative oncology group performance status \< 1 Exclusion Criteria: * Prior radiation and systemic therapy for a head and neck cancer. * Oral cavity cancer that is not amenable to surgical resection or the patient is not a surgical candidate. * Active or prior documented autoimmune or inflammatory disorders that have been treated with steroids or immunomodulator therapy in the past 5 years. Exceptions: Patients with vitiligo, type 1 diabetes mellitus, and endocrinopathies (including hypothyroidism due to autoimmune thyroiditis) only requiring hormone replacement, childhood asthma that is resolved, or psoriasis it does not require systemic treatment are permitted. * Conditions requiring systemic treatment with either corticosteroids (\> 10 mg daily prednisone equivalents) or other immunosuppressant medications within 14 days of treatment on study. * Receipt of live attenuated vaccine within 30 days prior initiating treatment on study. * Prior allogeneic stem cell transplantation, or autologous stem cell transplantation. * Any infection requiring hospitalization and/or intravenous antibiotic therapy within 2 weeks of the start of treatment. * Uncontrolled infection with human immunodeficiency virus (HIV), hepatitis B or hepatitis C virus (HBV or HCV) infection; or diagnosis of immunodeficiency. 1. Patients with known HIV infection who have controlled infection (undetectable viral load (HIV RNA PCR) and CD4 count above 350, either spontaneously or on a stable antiviral regimen) are permitted. For patients with controlled HIV infection monitoring will be performed per local standards 2. Patients with HBV (hepatitis B surface antigen positive; HBsAg+) who have controlled infection (serum HBV DNA PCR that is below the limit of detection and receiving anti-viral therapy for HBV) are permitted. Patients with controlled infections must undergo periodic monitoring of HBV DNA. Patients must remain on anti-viral therapy for at least 6 months be on the last dose of Cemiplimab. 3. Patients were HCV antibody positive (HCV Ab+) who have controlled infection (undetectable HCV RNA by PCR, either spontaneously or in response to successful prior course of anti-HCV therapy) are permitted. * History of immune-related pneumonitis with the last 5 years. * History of interstitial lung disease (e.g., idiopathic pulmonary fibrosis, organizing pneumonia) or active, noninfectious pneumonitis that required immune-suppressive doses of leuko-corticoids to assist with management. * Known hypersensitivity or allergy to any of the excipients in the cemiplimab drug product. * Patients with a history of solid organ transplant (exception: corneal transplant) * Any medical comorbidity, physical examination finding, or metabolic dysfunction, or clinical laboratory abnormality that in the opinion of the investigator renders the patient unsuitable for participation in a clinical trial due to high safety risks. * Women with a positive serum or urine beta-hCG pregnancy test at screening/baseline visit. If positive, pregnancy must be ruled out by ultrasound for patient to be eligible. * Breast-feeding women * Women of childbearing potential who are sexually active and aren't willing to practice highly effective contraception prior to the first dose of Cemiplimab, during the study, and for at least 180 days after the last dose. Highly effective contraceptive measures include: 1. Stable use of combined estrogen and progesterone containing hormonal contraception or progesterone and-only hormonal contraception associated with inhibition of ovulation initiated 2 or more menstrual cycles prior to screening 2. Intrauterine device; intrauterine hormone-releasing system 3. Bilateral tubal ligation 4. Vasectomized partner and/or 5. Sexual abstinence