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

The purpose of this study is to find out whether combining the standard chemotherapy for head and neck cancer with the immunotherapy drugs cetuximab and cemiplimab (the study drug) is a safe treatment for head and neck cancer, and whether receiving this combination treatment before surgery may allow participants to forgo the standard radiation treatment after surgery.

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 \30 mL/min 5. Adequate hepatic function: * Total bilirubin \