Toripalimab With Chemotherapy for Sinus Cancer

Inclusion Criteria: * Participants must have histologically or cytologically confirmed locoregionally advanced nasal cavity or paranasal sinus cancer including the following histologic subtypes: squamous cell carcinoma (SCC) of any morphologic variation: verrucous, papillary, basaloid, spindle cell, and adenosquamous; or sinonasal undifferentiated carcinoma (SNUC). * Participants with SCC should have resectable disease at baseline per the discretion of the treating surgical oncologist(s). \*Participants with SNUC can have operable or borderline resectable (definition: resection would been morbid requiring extensive surgery and would have chances of incomplete gross total resection) disease as judged by the treating surgical oncologist(s). * Participants must have clinical stage disease as defined below using the 8th (2017) edition of the tumor, node, metastasis (TNM) staging system by the American Joint Committee on Cancer (AJCC) and the Union for International Cancer Control (UICC): * T2, N1-3 III * T3, any N III, IVA, IVB * T4, any N IVA, IVB * Participants must be willing to provide blood and tissue pre-treatment and at the time of surgery for pathologic and correlative analyses. * Age 18 years or older at the time of informed consent. * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. * Participants must have adequate organ and marrow function as defined below: * Absolute neutrophil count ≥1000/mcL * Platelets ≥100 * Total bilirubin ≤institutional upper limit of normal (ULN) * AST(SGOT) / ALT (SGPT) ≤3x ULN * Creatinine ≤institutional ULN or GFR of ≥50 mL/min/1.73 m2 unless data exists supporting safe use at lower kidney function values, no lower than 30 mL/min/1.73 m2 * Women of child-bearing potential (WOCBP) and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Contraception use should be maintained until at least 6 months after the last dose of chemotherapy for females and 3 months for males. In addition, contraception use should continue until 4 months after last dose of toripalimab for both males and females. * Ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: * Participants with nasal cavity or paranasal sinus malignancies demonstrating histologies other than SCC or SNUC in the opinion of the reviewing pathologist. Excluded subtypes include: angiosarcomas, rhabdomyosarcomas, lymphomas, olfactory neuroblastomas (esthesioneuroblastomas), melanomas, and meningiomas among others. SNEC or sinonasal neuroendocrine carcinoma is not permitted. * Participants with unresectable or inoperable disease as judged by the treating surgical oncologist(s). * Participants with known distant metastatic disease (M1 or IVC). * Has received prior therapy with an anti-PD-1/L1 agent or any other agent directed to another stimulatory or co-inhibitory T-cell receptor. * Has received a live vaccine or live-attenuated vaccine within 30 days prior to the first dose of study drug. Non-live vaccines are permitted. * Carries a diagnosis of immunodeficiency or is receiving chronic systemic corticosteroid therapy (in doses exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to the first dose of study drug. * Has a known additional malignancy that is progressing or has required active treatment within the past 2 years. Participants with basal cell carcinoma of the skin, squamous cell carcinoma of the skin or carcinoma in situ (breast carcinoma, cervical cancer in situ) that have undergone potentially curative therapy are not excluded. Exceptions may be permitted at the discretion of the overall Sponsor-Investigator. * Has an active autoimmune disease that has required systemic treatment in past 6 months (with use of a disease modifying agents, corticosteroids, or immunosuppressive drugs). Replacement therapy (thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not considered a form of systemic treatment and is permitted. * Has a history of (non-infectious) pneumonitis or interstitial lung disease that required steroids or has current pneumonitis or interstitial lung disease. * Has a known history of human immunodeficiency virus (HIV) infection that is uncontrolled. No HIV testing is required unless mandated by local health authority. Patients with well controlled HIV may be eligible if their CD4 T cell count is favorable and their HIV viral load is undetectable. * Has a known history of active Hepatitis B (defined as Hepatitis B surface antigen \[HBsAg\] reactive) or known active Hepatitis C virus (defined as HCV RNA \[qualitative\] is detected) infection. Note: no testing for Hepatitis B and Hepatitis C is required unless mandated by local health authority. * Has a history of allogeneic tissue or solid organ transplant. * Women who are pregnant or breastfeeding.