Neoadjuvant Chemotherapy and Programmed Cell Death Protein 1(PD-1) Inhibition for Head and Neck Cancer Treatment De-escalation (NeoScorch HN)

Inclusion: * Eligible subjects must have histologically confirmed, locoregionally advanced head and neck or sinonasal, nasolacrimal, or skull base tumors and meet HPV testing requirements as outlined. * HPV-independent HNSCC (cT2-cT4, N0-N3) with potential for organ preservation using response-adapted surgery. * HPV-associated HNSCC with radiographic extranodal extension (cT1-cT3 tonsil or lateralized base of tongue, N0-N1, up to 4 nodes with rENE). * Sinonasal/skull base tumors, including: sinonasal carcinomas, HPV-associated sinonasal cancer, sinonasal undifferentiated carcinoma (e.g., Isocitrate dehydrogenase 2 (IDH2) mutant), or neuroendocrine sinonasal tumors (e.g., olfactory neuroblastoma) (cT2-cT4, N0-N3). * HPV16 type only. Patients with non-HPV16 cancers are not eligible. If p16 immunohistohemistry (IHC) positivity is the only result available at enrollment, neoadjuvant therapy may start while HPV nucleic acid testing is pending. Patients found to be HPV non-16 must discontinue study participation. * At least 8 unstained 5-µm slides must be available. If unavailable, a new biopsy is required unless waived by the PI. * Appropriate candidates for curative-intent therapy. * American Joint Committee on Cancer (AJCC) 7th edition: Stage III-IV, excluding N2c or bulky N2b/c (N3 equivalent) and bulky T4 (≥30cc). * AJCC 8th edition: Stage I with N1, Stage II, or Stage III, excluding N2 disease, bulky nodal disease (N3 equivalent), or bulky T4 (≥30cc). * Surgical arm: Candidates must be operable based on upfront imaging/exam. Patients with Grade 1 rENE may proceed to surgery; Grade 2/3 rENE are excluded. * Measurable disease per RECIST 1.1. * No prior systemic therapy, radiotherapy, or investigational agents for the current cancer. * No complete surgical resection within 8 weeks of enrollment (biopsy or excision with residual disease acceptable). * Eastern Cooperative Oncology Group (ECOG) 0-1 or Karnofsky ≥70%. * Platelets ≥100,000/µL. * Absolute Neutrophil Count (ANC) ≥1,500/µL. * Hemoglobin ≥9 g/dL (without recent transfusion/EPO). * Aspartate Aminotransferase (AST)/ Alanine Aminotransferase (ALT) \<2.5 × ULN. * Albumin ≥2.5 mg/dL. * Total bilirubin ≤1.5 × ULN or direct bilirubin ≤ULN if total \>1.5 × ULN (Upper Limit of Normal). * Creatinine clearance ≥60 mL/min (Cockcroft-Gault or measured GFR). * International Normalized Ratio (INR)/ Prothrombin Time (PT) ≤1.5 × ULN (unless on anticoagulants; must be within therapeutic range). * Activated Partial Thromboplastin Time (aPTT) ≤1.5 × ULN (unless on anticoagulants; must be within therapeutic range). * Must sign and understand a study-specific informed consent form. * Women of childbearing potential (WOCBP): Negative pregnancy test within 72 hours prior to first dose. * WOCBP must not be breastfeeding and must agree to use highly effective contraception during therapy and for 120 days after last dose. * Men: Must use adequate contraception during treatment and for 120 days after last dose; condom use required in addition to highly effective methods. * Azoospermic men and WOCBP not heterosexually active are exempt from contraception but must still undergo pregnancy testing. * Counseling on pregnancy prevention is mandatory. * Highly effective methods (\<1% failure rate with consistent use) must be used Exclusion: * WOCBP with a positive urine pregnancy test within 72 hours before treatment allocation; if positive or inconclusive, a confirmatory serum pregnancy test is required. * Pregnant or breastfeeding, or planning to conceive or father a child during the study and for 120 days after the last dose. * Prior treatment with PD-1, PD-L1, PD-L2 inhibitors, or other agents targeting T-cell receptors (e.g., Cytotoxic T-lymphocyte antigen 4 (CTLA-4), OX40 (Tumor Necrosis Factor Receptor Superfamily Member 4), CD137). * Prior systemic anti-cancer therapy or radiotherapy for the current cancer. Surgery is allowed if adequately recovered from complications. * Radiotherapy within 2 weeks of study start. A 1-week washout is permitted for palliative, non-stereotactic radiation (≤2 weeks) to non-Central Nervous System (CNS), non-head and neck disease, provided there are no residual toxicities, no steroid requirement, and no history of radiation pneumonitis. * Live or live-attenuated vaccines within 30 days of first study dose (including live Corona Virus Disease (COVID-19) vaccines). Inactivated, Messenger ribonucleic acid (mRNA), and peptide vaccines are allowed. * Concurrent treatment with other investigational agents. * Participation in another investigational drug or device study within 4 weeks before first study dose, unless in follow-up phase only. * Diagnosis of immunodeficiency, or receiving chronic systemic steroids at doses \>10 mg prednisone equivalent daily, or other immunosuppressive therapy within 7 days before study drug. * Active autoimmune disease requiring systemic treatment in the past 2 years. Physiologic replacement therapy (thyroxine, insulin, low-dose steroids for adrenal or pituitary insufficiency) is allowed. * History of severe hypersensitivity (≥Grade 3) to Toripalimab, its excipients, or other anti-PD-1 agents. * Additional active malignancy requiring treatment within 2 years, except basal/squamous cell skin cancers, in situ cancers, low-grade tumors unlikely to affect survival within 3 years, or cancers treated with curative therapy. * Active CNS metastases or carcinomatous meningitis. Intracranial extension of the primary tumor is allowed. Patients with previously treated brain metastases may enroll if radiologically stable ≥4 weeks, clinically stable, and off steroids ≥14 days before study drug. * History of pneumonitis or interstitial lung disease requiring steroids, or current pneumonitis/Interstitial Lung Disease (ILD). * Active infection requiring systemic therapy. * Known HIV infection. * Known active Hepatitis B (HBsAg positive) or active Hepatitis C (HCV RNA positive). Patients with cleared or eradicated Hepatitis B (HBV) or HCV are eligible. * Any condition, therapy, or abnormality that could confound study results, interfere with participation, or be judged by the investigator as not in the participant's best interest. * Known psychiatric illness or substance abuse that could interfere with study compliance. Stable chronic managed disorders are acceptable. * History of allogeneic tissue or solid organ transplant. * Significant cardiovascular disease, including congestive heart failure (NYHA Class III or IV), unstable angina, serious uncontrolled arrhythmia, myocardial infarction within 6 months, or prior myocarditis.