This pilot clinical trial studies the side effects of nivolumab, ipilimumab and radiation therapy in treating patients with stage IVA-B head and neck cancer. Monoclonal antibodies, such as nivolumab and ipilimumab, may interfere with the ability of tumor cells to grow and spread. Radiation therapy uses high energy x-rays to kill tumor cells and shrink tumors. Giving nivolumab, ipilimumab, and radiation therapy may work better in treating patients with stage IVA-B head and neck cancer.

PRIMARY OBJECTIVES:

I. To investigate the safety of the combination of nivolumab and ipilimumab with radiation treatment for definitive management of patients with locally advanced squamous cell carcinoma of the head and neck.

SECONDARY OBJECTIVES:

I. To estimate the 1 year progression-free survival (PFS) in all patients treated.

II. To assess the overall response rate and overall survival of patients at one year

TERTIARY OBJECTIVES:

I. To explore whether PDL1 expression is associated with treatment response. II. To explore whether there is a net change in the Th1/Th2 ratio (IFN-gamma, IL-4, IL10, etc) or cell subset frequencies (M2 monocytes, myeloid-derived suppressor cells, etc) within a patient's peripheral blood either at baseline or in response to treatment is associated with treatment response.

III. To explore whether exosomes or other immune related serum biomarkers change after combination therapy.

Inclusion Criteria:

• Patients must be 18 years of age and older
• Pathologically confirmed squamous cell carcinoma of the head and neck (SCCHN), not previously treated
• Stage III-IVB disease of 1) oral cavity, 2) HPV-negative (p16-) oropharynx, 3) larynx, 4) hypopharynx
• Oropharyngeal primaries that are HPV-mediated (p16+) must be stage II-III. Stage II pateints must be either N2 or, if T3N0 or T3N1 they must also have at least 20 pack year history of smoking
• Tumor sample must be available for HPV p16 and PD-L1 testing
• Eastern Cooperative Oncology Group (ECOG) performance status 0-1
• White blood cells 2000/ul or more
• Absolute neutrophil count 1500/ul or more
• Platelets 100,000/ul or more
• Hemoglobin 9 g/dl or more
• Bilirubin less than or equal to 1.5 x the upper limit of normal (except subjects with Gilbert syndrome, who can have total bilirubin < 3 mg/dl)
• Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) less than or equal to 3 x the upper limit of normal
• Glomerular filtration rate (GFR) greater than or equal to 40 ml/min using the Cockcroft-Gault formula or Serum creatinine less than or equal to 1.5 x upper limit of normal (ULN)
• Women of reproductive potential should have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of human chorionic gonadotropin [HCG]) within 24 hours of the start of study drugs
• Women of reproductive potential must use highly effective contraception methods to avoid pregnancy for 23 weeks after the last dose of study drugs; "women of reproductive potential" is defined as any female who has experienced menarche and who has not undergone surgical sterilization (hysterectomy or bilateral oophorectomy) or who is not postmenopausal; menopause is defined clinically as 12 months of amenorrhea in a woman over 45 in the absence of other biological or physiological causes; in addition, women under the age of 55 must have a documented serum follicle stimulating hormone (FSH) level more than 40 mIU/mL
• Men of reproductive potential who are sexually active with women of reproductive potential must use any contraceptive method with a failure rate of less than 1% per year; men who are receiving the study medications will be instructed to adhere to contraception for 31 weeks after the last dose of study drugs; men who are azoospermic do not require contraception
• Informed consent: all subjects must be able to comprehend and sign a written informed consent document

Exclusion Criteria:

• Primary nasopharyngeal carcinoma
• Patients with brain metastases
• Patients who have participated in a study with an investigational agent or device within 2 weeks of initiation of treatment
• Any prior radiotherapy to the neck
• Patients with known contraindications to radiotherapy, including inherited syndromes associated with hypersensitivity to ionizing radiation (e.g., Ataxia-Telangiectasia, Nijmegen Breakage Syndrome)
• Any prior chemotherapy or radiation therapy for the current diagnosis
• Any prior therapy with anti-PD-1, anti-PD-L2, anti-CTLA-4 antibody, or any other antibody or drug specifically targeting T-cell co-stimulation or immune checkpoint pathways
• Any history of a sever hypersensitivity reaction to any monoclonal antibody
• Any history of allergy to the study drug components
• Any concurrent malignancies- exceptions include- basal cell carcinoma of the skin, squamous cell carcinoma of the skin, superficial bladder cancer or in situ cervical cancer that has undergone potentially curative therapy; patients with a history of other prior malignancy must have been treated with curative intent and must have remained disease-free for 3 years post-diagnosis
• Any diagnosis of immunodeficiency or current immunosuppressive therapy including >10mg/day of prednisone within 14 days of enrollment is not permitted
• Patients that have an active autoimmune disease requiring systemic treatment within the past 3 months or a documented history of clinically severe autoimmune disease, or a syndrome that requires systemic steroids (> 10 mg daily prednisone equivalents) or immunosuppressive agents; subjects with vitiligo, type I diabetes mellitus, or resolved childhood asthma/atopy would be an exception to this rule. Inhaled or topical steroids, and adrenal replacement steroids \