Testing the Addition of Cemiplimab (REGN2810) to Chemotherapy Treatment Given Prior to Surgery in Patients With Sinonasal Squamous Cell Carcinoma

Inclusion Criteria: * Patients must have histologically confirmed squamous cell carcinoma of sinonasal origin * Patients must have a T stage (T3, T4a, and select T4b) primary tumor according to American Joint Committee on Cancer (AJCC) 8th edition. Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as ≥ 20 mm (≥ 2 cm) by chest x-ray or as ≥ 10 mm (≥ 1 cm) with CT scan, MRI, or calipers by clinical exam * No evidence of metastatic disease determined by pre-treatment imaging. Metastatic disease to neck nodes is considered locally advanced and therefore allowable. Patients with N0 and N1-3 disease will be eligible * Known HPV status (i.e., HPV negative, p16 immunohistochemistry \[IHC\] positive, high risk \[HR\]-HPV in situ hybridization \[ISH\] positive) from testing performed prior to referral. HPV status data (e.g., date of test, type of test \[p16 IHC or HR-HPV ISH\] and testing result) must be collected during enrollment. Patients who do not have this information available for collection will not be enrolled on this study * Age ≥ 18 years * Because no dosing or adverse event data are currently available on the use of cemiplimab (REGN2810) in combination with carboplatin and paclitaxel in patients \< 18 years of age, children are excluded from this study * Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2 (Karnofsky ≥ 60%) * Hemoglobin ≥ 8 g/dL (acceptable to reach via transfusion) * Absolute neutrophil count ≥ 1,500/mcL * Platelets ≥ 100,000/mcL * Total bilirubin ≤ 1.5 × institutional upper limit of normal (ULN) * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) ≤ 3 × institutional ULN * Creatinine clearance ≥ 40 mL/min * Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial * For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated * Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load * Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial * Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class II or better * Based on its mechanism of action, cemiplimab (REGN2810) can cause fetal harm when administered to a pregnant woman. Animal studies have demonstrated that inhibition of the PD-1/PD-L1 pathway can lead to increased risk of immune-mediated rejection of the developing fetus resulting in fetal death. For this reason and because paclitaxel is a class D agent with the potential for teratogenic or abortifacient effects, women of childbearing potential (WCBP) and men should use highly effective contraception during treatment and for 6 months after the last dose of the study drugs. WCBP and men should avoid donating eggs/sperm during treatment and for 6 months after the last dose of the study drugs. Women should discontinue nursing during treatment and for 6 months after the last dose of the study drugs * Ability to understand and the willingness to sign a written informed consent document. Legally authorized representatives may sign and give informed consent on behalf of study participants * Prior to enrollment, verification of payment coverage by insurance (or other payment) for neoadjuvant paclitaxel and carboplatin chemotherapy must be obtained Exclusion Criteria: * Patients with unresectable disease * Patients presenting with T3 disease without the need for maxillectomy and/or orbital invasion requiring orbital dissection/resection * Patients who have had any previous systemic therapy to the index lesion in the past 12 months. This includes cemiplimab (REGN2810) and/or other immune modulating agents. Previous systemic therapy may alter or affect response * Patients who had palliative RT (\< 20 Gy) within 1 week prior to entering the study * Ongoing or recent (within 5 years) evidence of significant autoimmune disease that required treatment with systemic immunosuppressive treatments, which may suggest risk for immune-mediated adverse events (imAEs) * History of pneumonitis within the last 5 years * Patients who have not recovered from adverse events (AEs) due to prior anti-cancer therapy (i.e., have residual toxicities \> grade 1) with the exception of alopecia * Patients who are receiving any other investigational agents * History of allergic reactions attributed to compounds of similar chemical or biologic composition to cemiplimab (REGN2810) or carboplatin and paclitaxel * Patients with uncontrolled intercurrent illness or any other significant condition(s) that would make participation in this protocol unreasonably hazardous * Pregnant women are excluded from this study because of the increased risk of immune-mediated rejection of the developing fetus with cemiplimab (REGN2810). Men and WCBP who are not prepared to use highly effective contraception during and for 6 months after completion of treatment are excluded from this study