• 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.