Induction Chemotherapy Followed By Cetuximab and Radiation in HPV-Associated Resectable Stage III/IV Oropharynx Cancer

Inclusion Criteria:

* Histologically or cytologically confirmed squamous cell carcinoma of the oropharynx as determined by Hematoxylin and eosin (H\&E) staining

  * Newly diagnosed disease
  * Resectable disease OR disease that is expected to become resectable after study treatment
  * Stage III, IVA, or IVB disease as determined by imaging studies (computed tomography (CT) scan with IV contrast or magnetic resonance imaging (MRI) required) and a complete head and neck exam
* Paraffin-embedded tumor specimen available for central confirmation of HPV-associated disease as determined by H\&E staining and in-situ hybridization (ISH) for HPV-16 and immunohistochemistry (IHC) for p16

  * HPV-associated disease is defined as p16 IHC-positive and/or HPV-16 ISH-positive
  * Non-HPV-associated disease is defined as p16 IHC-negative
  * NOTE: If there is limited tumor material, p16 IHC will be performed before HPV-16 ISH
* Measurable disease of the primary tumor or nodes by clinical and radiographic methods, defined as a lesion that is ≥ 2 cm in at least one dimension by clinical exam AND by radiographic exam with CT scan or MRI (or a lesion that is ≥ 1 cm in at least one dimension if the radiographic exam utilizes spiral CT scan)
* No primary tumor or nodal metastasis fixed to the carotid artery, skull base, or cervical spine
* No evidence of distant metastases
* Eastern Cooperative Oncology Group performance status 0-1
* Granulocytes ≥ 1,000/mm\^3
* Platelet count ≥ 100,000/mm\^3
* Total serum bilirubin ≤ 1.5 mg/dL
* Creatinine clearance ≥ 60 mL/min
* Negative pregnancy test
* Fertile patients must use effective contraception
* No history of another malignancy (except for carcinoma in situ of the cervix and/or nonmelanomatous skin cancer) unless it has been curatively treated and the patient has been disease-free for ≥ 2 years
* Patients with any of the following within the past 6 months are eligible provided they have been evaluated by a cardiologist and/or neurologist before study entry:

  * New York Heart Association (NYHA) class III-IV congestive heart failure
  * Cerebrovascular accident or transient ischemic attack
  * Unstable angina
  * Myocardial infarction (with or without ST elevation)

Exclusion Criteria:

* Prior chemotherapy
* Prior radiotherapy above the clavicles
* Prior surgery with curative intent for this disease (complete head and neck exam with biopsy allowed)
* Prior therapy specifically and directly targeting the EGFR pathway
* Prior severe infusion reaction to a monoclonal antibody
* Uncontrolled diabetes, uncontrolled infection despite antibiotics, or uncontrolled hypertension within the past 30 days
* Concurrent illness likely to interfere with study therapy or to prevent surgical resection
* Pregnant or nursing