This phase Ib trial studies the side effects and best dose of ipilimumab when given together with cetuximab and intensity-modulated radiation therapy (IMRT) in treating patients with previously untreated stage III-IVB head and neck cancer. Monoclonal antibodies, such as ipilimumab and cetuximab, may block tumor growth in different ways by targeting certain cells. Specialized radiation therapy, such as IMRT, that delivers a high dose of radiation directly to the tumor may kill more tumor cells and cause less damage to normal tissue. Giving ipilimumab together with cetuximab and IMRT may kill more tumor cells.

PRIMARY OBJECTIVES:

I. To identify the starting dose of ipilimumab, in combination with standard cetuximab-IMRT in patients with high- or intermediate-risk, locally advanced head and neck squamous cell carcinoma (HNSCC), for use in a future clinical efficacy trial.

SECONDARY OBJECTIVES:

I. To estimate the clinical response of patients with high- or intermediate-risk, locally advanced HNSCC treated with above regimen using Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria.

II. To estimate the 2-year progression-free survival of patients with high- or intermediate-risk, locally advanced HNSCC treated with the above regimen.

III. To investigate serum, lymphocyte and tissue biomarkers as predictors of progression-free survival, toxicity and other outcome parameters in patients with high- or intermediate-risk, locally advanced HNSCC treated with above regimen.

IV. To estimate the association by dose-response modeling between dose of ipilimumab, clinical response and biomarkers.

OUTLINE: This is a dose-escalation study of ipilimumab.

Patients receive cetuximab intravenously (IV) over 60-120 minutes on days 1, 8, 15, and 22. Treatment with cetuximab repeats every 4 weeks for 2 courses. Beginning in week 2 of course 1, patients undergo concurrent IMRT 5 days per week for 7 weeks. Beginning in week 4 (day 1 of course 2) patients also receive ipilimumab IV over 90 minutes once every 21 days for 3 courses. Treatment continues in the absence of disease progression or unacceptable toxicity. Patients achieving disease progression may undergo surgery after completion of therapy.

After completion of study treatment, patients are followed up every 12 weeks for 1 year, every 6 months for 1 year, and then every 12 months for 3 years.

Inclusion Criteria:

• American Joint Committee on Cancer (AJCC) stage III/IVB, excluding T1N1, histologically or cytologically confirmed squamous cell carcinoma or undifferentiated carcinoma of the head and neck; patients should not have distant metastasis; primary sites include: oropharynx, hypopharynx, larynx

• Patients must have high or intermediate risk disease, defined as follows:

  • High risk: non-oropharyngeal subsite including larynx or hypopharynx (p16 status not required) or human papilloma virus (HPV)/p16- oropharynx subsite
  • Intermediate risk: HPV/p16+ oropharyngeal squamous cell cancer with: >= 10 pack (pk)-year (yr) smoking history and >= N2 nodal disease, or the presence of T4 tumor or N3 nodal disease, irrespective of smoking status

• 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 computed tomography (CT) scan, magnetic resonance imaging (MRI), or calipers by clinical exam

• Patients should be newly diagnosed HNSCC, with no prior therapy for this disease

• Eastern Cooperative Oncology Group (ECOG) performance status typically =< 1 (Karnofsky >= 70%)

• Leukocytes >= 3,000/mcL

• Absolute neutrophil count >= 1,200/mcL

• Platelets >= 75,000/mcL

• Total bilirubin =< 2 mg/dL (=< 3 mg/dL in case of Gilbert's syndrome)

• Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =< 2 times institutional upper limit of normal (IULN)

• Creatinine clearance >= 40 mL/min/1.73 m^2

• Patients must have the ability to understand and to sign written informed consent

Exclusion Criteria:

• Patients who have had prior chemotherapy, radiotherapy, or surgery with curative intent for HNSCC
• Patients with a history of prior treatment with ipilimumab, anti-programmed cell death 1 (PD 1) antibody, cluster of differentiation 137 (CD137) agonist or other immune activating therapy such as anti-cluster of differentiation 40 (CD 40) antibody
• Patients who are receiving any other investigational agents
• Autoimmune disease: patients with a history of inflammatory bowel disease, including ulcerative colitis and Crohn's disease, are excluded from this study, as are patients with a history of symptomatic non-gastrointestinal autoimmune disease (e.g., rheumatoid arthritis, systemic progressive sclerosis [scleroderma], systemic lupus erythematosus, autoimmune vasculitis [e.g., Wegener's granulomatosis]); central nervous system (CNS) or motor neuropathy considered of autoimmune origin (e.g. Guillain-Barre syndrome and myasthenia gravis, multiple sclerosis)
• Patients with known immunodeficiency disorder, or presumed to be unable to respond to anti-cytotoxic T-lymphocyte-associated protein 4 (CTLA 4) monoclonal antibody (mAb)
• Patients with distant metastatic disease (stage IVC)
• History of allergic reactions attributed to compounds of similar chemical or biologic composition to cetuximab or ipilimumab
• Patient is < 2 years free from a second primary malignancy unless the other malignancy is non-melanomatous skin cancer or an in-situ tumor treated with curative intent
• Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements; patients with chronic hepatitis B or hepatitis C infections are excluded
• Pregnant women are excluded from this study
• Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible