Window of Opportunity in Preserving Laryngeal Function Trial

Inclusion Criteria: 1. Pathologically confirmed and previously untreated squamous cell carcinoma of the larynx or hypopharynx 2. AJCC 8th Edition Stage III - IV disease (T1-T2/N1-N3, T3-T4/N0-N3) 3. Disease (primary \& nodal) must be potentially surgically resectable and curable with conventional surgery and CRT 4. ECOG PS 0 - 2 5. Sexually active fertile subjects and their partners must agree to use highly effective method of contraception prior to study entry, during the course of the study, and for 1 year after the last dose of treatment (whichever is later). An additional contraceptive method, such as a barrier method (e.g., condom), is required. In addition, men must agree not to donate sperm and women must agree not to donate eggs (ova, oocyte) for the purpose of reproduction during these same periods. 6. Female subjects of childbearing potential must not be pregnant or breastfeeding at screening. Female subjects are considered to be of childbearing potential unless one of the following criteria is met: Permanent sterilization (hysterectomy, bilateral salpingectomy, or bilateral oophorectomy) or documented postmenopausal status (defined as 12 months of amenorrhea in a woman \> 45 years-of-age in the absence of other biological or physiological causes). Note: Documentation may include review of medical records, medical examination, or medical history interview by study site staff. 7. Must have normal organ and marrow function as defined below: * Hemoglobin ≥ 9.0 g/dL * Absolute neutrophil count ≥ 1,500/mcL * Platelet count ≥ 100,000/mcL * Total bilirubin ≤ 1.5 X the institutional upper limit of normal (ULN) * AST (SGOT) ≤ 2.5 X institutional upper limit of normal (ULN) * ALT (SGPT) ≤ 2.5 X institutional ULN * Creatinine clearance ≥ 40 mL/min/1.73 m2 for patients with a creatinine level above institutional normal 8. Must have the ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: 1. Prior treatment for head and neck cancer 2. Unresectable laryngeal or hypopharyngeal squamous cell carcinoma 3. Distant metastatic disease 4. Has an active autoimmune disease requiring systemic treatment within the past 3 months, or a syndrome that requires ongoing systemic steroids or immunosuppressive agents. Subjects with vitiligo, Grave's disease, or psoriasis not requiring systemic therapy or resolved childhood asthma/atopy would be an exception to this rule. Subjects that require intermittent use of bronchodilators or local steroid injections would not be excluded from the study. Subjects with hypothyroidism or Sjogren's syndrome will not be excluded from the study. 5. Has a history of non-infectious pneumonitis that required steroids, evidence of interstitial lung disease, or currently active non-infectious pneumonitis. 6. Known allergy or hypersensitivity to carboplatin or cisplatin, toripalimab, or paclitaxel. 7. Prior malignancy within 2 years that in the investigator's opinion would be likely to affect the outcomes for the patient. 8. Peripheral sensory neuropathy \> grade 2 by CTCAE v5.0 9. Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator. 10. Has acute or chronic active hepatitis B and C virus infection or known history of untreated hepatitis B (defined as hepatitis B surface antigen \[HBsAg\] reactive) or known active hepatitis C virus (HCV) (defined as HCV RNA \[qualitative\]) or HIV infection (see note). 1. Note: No testing for Hepatitis B, Hepatitis C, or HIV is required unless mandated by local health authority or clinically indicated. 2. Note: Participants with a history of HIV infection are considered eligible if CD4+ T cell counts are ≥350 cells/µL and the patient has had no opportunistic infections in the last 12 months.