A Trial of Locoregionally Advanced Squamous Cell Carcinoma of The Head and Neck

Inclusion Criteria: * Newly diagnosed, pathologically proven, treatment-naïve unresected LA-HNSCC * Stage T3-T4 \[N0-N3\] or any N2a-3 \[T1-T4\] larynx, hypopharynx, oral cavity, or p16(-) oropharynx (AJCC 8th edition staging) * Stage T4 or N3 p16(+) oropharynx (AJCC 8th edition staging) * 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 with conventional techniques or as ≥10 mm with spiral CT scan, MRI, or calipers by clinical exam. RECIST 1.1 criteria * No previous radiation or chemotherapy for head and neck cancer. * No complete surgical resection for a head and neck cancer within 8 weeks of enrollment (although lymph node biopsy including excision of an individual node with presence of residual nodal disease, or surgical biopsy/excision of the tumor with residual measurable disease is acceptable.) * If a primary oropharyngeal squamous cell carcinoma is diagnosed, HPV status must be assessed by immunohistochemistry for p16 expression prior to enrollment. Confirmatory HPV assessment with HPV ISH or HPV PCR should also be completed, however, this is not required for enrollment. * Patients must be at least 18 years of age. Because no dosing or adverse event data are currently available on the use of Cemiplimab in combination with Fianlimab in patients \<18 years of age, children are excluded from this study. * ECOG performance status 0-1 * Patients must have adequate organ and marrow function as defined below). * Leukocytes ≥3,000/mcL * Absolute neutrophil count ≥1,500/mcL * Platelets ≥100,000/mcL * Hemoglobin ≥ 9.0 gm/dL * Total bilirubin within normal institutional limits * AST(SGOT)/ALT(SGPT) ≤2.5 × institutional upper limit of normal * Albumin \> 2.9 gm/dL * Creatinine Creatinine clearance \> 45 mL/min, normal within 2 weeks prior to start of treatment (Of note, the standard Cockcroft and Gault formula must be used to calculate CrCl for enrollment or dosing). * 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 2B or better. * Women of childbearing potential (WOCBP) must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of HCG) within 24 hours prior to the start of study drug. WOCBP are defined as women who are fertile following menarche until becoming postmenopausal, unless permanently sterile. Permanent sterilization methods include hysterectomy, bilateral salpingectomy, and bilateral oophorectomy. A postmenopausal state is defined as no menses for 12 months without an alternative medical cause. A high FSH level in the postmenopausal range may be used to confirm a postmenopausal state in women not using hormonal contraception or hormonal replacement therapy. However, in the absence of 12 months of amenorrhea, a single FSH measurement is insufficient to determine the occurrence of a postmenopausal state. The above definitions are according to the CTFG guidance. Pregnancy testing and contraception are not required for women with documented hysterectomy or tubal ligation. * Women must not be breastfeeding. * WOCBP must agree to follow instructions for method(s) of contraception for the duration of treatment with study drug(s) plus 6 months after completing chemoradiation or receiving the last dose of cemiplimab or fianlimab, whichever occurs latest. Pregnancy occurring in a female patient or female partner of a male patient during the study must be reported to the study investigators. If a woman were to become pregnant while taking the study drugs, treatment should be discontinued and pregnancy should be followed until outcome. * WOCBP must agree not to donate eggs (ova, oocytes) for the purposes of assisted reproduction during the entire trial and until 6 months after last treatment. * Men who are sexually active with women of childbearing potential must agree to follow instructions for method(s) of contraception for the duration of treatment with study drug(s) plus 6 months after completing the last dose of cemiplimab or fianlimab, whichever occurs latest. Vasectomized partner or vasectomized study participant must have received medical assessment of the surgical success. * All men must agree not to donate sperm during the trial and for 6 months after receiving the last therapy dose * Patients must sign a study-specific informed consent form prior to study entry. Patients should have the ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Unequivocal demonstration of distant metastatic disease (M1 disease). * Unidentifiable primary site. * Patients who are receiving any other investigational agents. * Prior surgical therapy other than incisional/excisional biopsy or organ-sparing procedures such as debulking of airway-compromising tumors. Residual measurable tumor is required for enrollment as discussed above. * Prior systemic anti-cancer treatment within the last 8 weeks. * Has had a prior anti-cancer monoclonal antibody (mAb) within 4 weeks prior to study Day 1 or who has not recovered (i.e., ≤ Grade 1 or at baseline) from adverse events due to agents administered more than 4 weeks earlier. * Has a known additional malignancy that is progressing or requires active treatment. Exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer or any tumors that are not likely to influence life expectancy in the subsequent 3 years without active treatment. Patients are not considered to have a "currently active" malignancy if they have completed therapy and are free of disease for ≥ 3 years. * Active medical illness(es) which would impair patient tolerance to therapy or limit survival. This includes but is not limited to ongoing or active infection, immunodeficiency, symptomatic congestive heart failure, pulmonary dysfunction, cardiomyopathy, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance. Patients with clinically stable and/or chronically managed medical illnesses that are not symptomatic and/or are not expected to impact treatment on protocol are still eligible (conditions to be reviewed by the PI to confirm eligibility). * Exclusions related to infection or immunodeficiency * History or current evidence of significant (CTCAE grade ≥2) local or systemic infection (eg, cellulitis, pneumonia, septicemia) requiring systemic antibiotic treatment within 2 weeks prior to the first dose of trial medication. * Active infection requiring therapy. * Ongoing or recent (within 2 years) evidence of an autoimmune disease that required systemic treatment with immunosuppressive agents. The following are non-exclusionary: vitiligo, childhood asthma that has resolved, residual hypothyroidism that requires only hormone replacement, psoriasis not requiring systemic treatment. Replacement therapy e.g. levothyroxine, insulin, or physiologic corticosteroid doses for adrenal or pituitary insufficiency, etc. are not considered a form of systemic treatment. * Uncontrolled infection with HIV, HBV, or HCV infection; or diagnosis of immunodeficiency that is related to, or results in chronic infection. * Patients with known HIV who have controlled infection (undetectable viral load and CD4 count above 350 either spontaneously or on a stable antiviral regimen) are permitted. For patients with controlled HIV infection, monitoring will be performed per local standards. * Patients with known hepatitis B (HepBsAg+) who have controlled infection (serum hepatitis B virus DNA PCR that is below the limit of detection AND receiving anti-viral therapy for hepatitis B) are permitted. Patients with controlled infections must undergo periodic monitoring of HBV DNA per local standards and must remain on anti-viral therapy for at least 6 months beyond the last dose of investigational study drug. * Patients who are known hepatitis C virus antibody positive (HCV Ab+) who have controlled infection (undetectable HCV RNA by PCR either spontaneously or in response to a successful prior course of anti-HCV therapy) are permitted. * Patients with HIV or hepatitis must be reviewed by a qualified specialist (eg, infectious disease or hepatologist) managing this disease prior to commencing and regularly throughout the duration of their participation in the trial * Diagnosis of immunodeficiency or is receiving systemic steroid therapy in excess of physiologic dose or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment. Physiologic replacement doses are allowed up to and including 10mg of prednisone/day or equivalent. Inhaled or topical steroids are permitted, if they are not for treatment of an autoimmune disorder. * Known history of active tuberculosis (Bacillus Tuberculosis infection). * Known history of, or any evidence of active, non-infectious pneumonitis. * Exclusions related to cardiac conditions: * Participants with a history of myocarditis. * TnT or troponin I TnI \> 2x institutional ULN at baseline. * Patients with TnT or TnI levels between \> 1 to 2x ULN are permitted if repeat levels within 24 hours are ≤ 1x ULN. If TnT or TnI levels are \> 1 to 2x ULN within 24 hours, the subject may undergo a cardiac evaluation and be considered for treatment by the investigator based on the medical judgement in the patient's best interest * 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. * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to cemiplimab, finalimab, or any other drug used in this protocol. * Pregnant women are excluded from this study because the effects of fianlimab (REGN3767) on reproductive organs in males and females are unknown. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with Cemiplimab with or without Fianlimab, breastfeeding should be discontinued if the mother is treated with Cemiplimab with or without Fianlimab. These potential risks may also apply to other agents used in this study. * Women of childbearing potential (WOCBP)\* who are unwilling to practice highly effective contraception prior to the initial dose/start of the first treatment, during the study, and for at least 6 months after the last dose. Highly effective contraceptive measures include: * Stable use of combined (estrogen and progestin containing) hormonal contraception (oral, intravaginal, transdermal) or progestogen-only hormonal contraception (oral, injectable, implantable) associated with inhibition of ovulation initiated 2 or more menstrual cycles prior to screening; * Intrauterine device; intrauterine hormone-releasing system. * Bilateral tubal occlusion/ligation. * Vasectomized partner (provided that the male vasectomized partner is the sole sexual partner of the WOCBP study participant and that the vasectomized partner has obtained medical assessment of surgical success for the procedure); and/or * Sexual abstinence†, ‡. Pregnancy testing and contraception are required for WOCBP. Pregnancy testing and contraception are not required for women who are post-menopausal or permanently sterile. \*WOCBP are defined as women who are fertile following menarche until becoming postmenopausal, unless permanently sterile. Permanent sterilization methods include hysterectomy, bilateral salpingectomy, and bilateral oophorectomy. A postmenopausal state is defined as no menses for 12 months without an alternative medical cause. A high FSH level in the postmenopausal range may be used to confirm a postmenopausal state in women not using hormonal contraception or hormonal replacement therapy. However, in the absence of 12 months of amenorrhea, a single FSH measurement is insufficient to determine the occurrence of a postmenopausal state. The above definitions are according to the CTFG guidance. †Sexual abstinence is considered a highly effective method only if defined as refraining from heterosexual intercourse during the entire period of risk associated with the study drugs. The reliability of sexual abstinence needs to be evaluated in relation to the duration of the clinical trial and the preferred and usual lifestyle of the subject. ‡Periodic abstinence (calendar, symptothermal, post-ovulation methods), withdrawal (coitus interruptus), spermicides only, and LAM are not acceptable methods of contraception. Female condom and male condom should not be used together. * Has received a live vaccine within 30 days of planned start of study therapy. Live or live attenuated vaccination with replicating potential. If a patient intends to receive a COVID-19 vaccine before the start of study drug, participation in the study should be delayed at least 1 week after any COVID-19 vaccination. During the treatment period, it is recommended to delay COVID-19 vaccination until patients are receiving and tolerating a steady dose of study drug. A vaccine dose should not be less than 48 hours before or after study drug dosing.