Sunitinib, Cetuximab, and Radiation Therapy in Treating Patients With Locally Advanced or Recurrent Squamous Cell Carcinoma of the Head and Neck

Inclusion Criteria: * Histologically or cytologically confirmed squamous cell carcinoma of the head and neck, meeting any of the following criteria: * Recurrent disease * Second primary locoregional recurrence\* with no clinically measurable distant disease * Poor prognosis non-metastatic head and neck carcinoma (M0) * Must have undergone radiotherapy as a component of prior treatment * Not a candidate for surgical resection with curative intent * Patients with high-risk features at resection or following resection for recurrence are eligible * Must have locoregional tumor amenable to radiotherapy or reirradiation with curative intent * Entire gross tumor recurrence volume must be able to be treated without exceeding a cumulative spinal cord dose of 50 Gy * Unresected tumors must be measurable according to RECIST * No known brain metastases * ECOG performance status (PS) 0-2 OR Karnofsky PS 60-100% * Life expectancy \> 12 weeks * WBC ≥ 3,000/mm\^³ * ANC \> 1,500/mm³ * Platelet count \> 100,000/mm³ * Total bilirubin \< 1.5 times upper limit of normal (ULN) * INR and PTT ratio \< 1.5 * AST and ALT ≤ 2.5 times ULN * Creatinine normal OR creatinine clearance \> 60 mL/min * Urine protein no more than trace * Hematocrit ≥ 28% * Hemoglobin ≥ 9 g/dL * QTc \< 500 msec * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * The following patients are eligible provided they have New York Heart Association class II cardiac function on baseline ECHO and MUGA: * Asymptomatic on treatment * Prior anthracycline exposure * Prior central thoracic radiotherapy included the heart in the radiotherapy port * No clinical evidence of active infection of any type, including hepatitis B or C virus * Infections controlled with therapy are allowed * Patients with hepatitis B or C on antiviral therapy with no detectable virus are allowed * No immune deficiency and/or HIV positivity * No history of allergic reactions attributed to compounds of similar chemical or biological composition to sunitinib malate * No gastrointestinal tract disease or condition, including any of the following, that impairs ability to retain sunitinib tablets: * Inability to take oral medication or a requirement for IV alimentation * Prior surgical procedures affecting absorption * Active peptic ulcer disease * None of the following conditions allowed: * Serious or nonhealing wound, ulcer, or bone fracture * Abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within the past 28 days * No significant concurrent medical or psychiatric illness which, in the opinion of the investigator, would interfere with the patient's ability to participate in the trial * No active carotid artery involvement * No history of documented thrombosis (pulmonary embolism within the past 12 months or deep vein thrombosis \[DVT\] within the past 6 months), known coagulopathies or thrombophilia, or evidence of DVT/thromboembolic event * No history of the following cardiovascular conditions : * Myocardial infarction within the past 12 months * Cardiac arrhythmia or serious ventricular arrhythmia (ventricular fibrillation or ventricular tachycardia ≥ 3 beats in a row) within the past 12 months * Stable/unstable angina within the past 12 months * Symptomatic congestive heart failure within the past 12 months * Coronary/peripheral artery bypass graft or stenting within the past 12 months * No cerebral vascular disease, cerebrovascular accident (stroke), or transient ischemic attack within the past 6 months * QTc prolongation (QTc interval ≥ 500 msec) * New York Heart Association class III-IV congestive heart failure * Poorly controlled hypertension (i.e., systolic blood pressure \[BP\] ≥ 140 mm Hg or diastolic BP ≥ 90 mm Hg) * Other significant ECG abnormalities * See Disease Characteristics * Recovered from all prior radiotherapy and chemotherapy * More than 4 months since prior radiotherapy to the head and neck * More than 2 weeks since prior hormone replacement therapy or hormonal contraceptives * More than 4 weeks since prior and no other concurrent investigational agents * At least 1 month since prior surgery (unless ambulatory within 48 hours) * At least 7 days since prior and no concurrent CYP3A4 inhibitors, including any of the following: * Azole antifungals (ketoconazole, itraconazole) * Clarithromycin * Erythromycin * Diltiazem * Verapamil * HIV protease inhibitors (indinavir, saquinavir, ritonavir, atazanavir, nelfinavir) * Delavirdine * At least 12 days since prior and no concurrent CYP3A4 inducers, including any of the following: * Rifampin * Rifabutin * Carbamazepine * Phenobarbital * Phenytoin * St. John wort * Efavirenz * Tipranavir * Concurrent coumarin-derivative anticoagulants (e.g., warfarin up to 2 mg daily) allowed for prophylaxis of thrombosis * Concurrent use of medications known to affect the conductive system (e.g., beta-blockers, calcium channel blockers, or digoxin) allowed under investigator supervision * No concurrent agent with proarrhythmic potential, including any of the following: * Terfenadine * Quinidine * Procainamide * Disopyramide * Sotalol * Probucol * Bepridil * Haloperidol * Risperidone * Indapamide * Flecainide * No concurrent chronic steroid treatment for \> 6 months (i.e., prednisolone doses \> 10 mg/day or equivalent) * No concurrent combination antiretroviral therapy for HIV-positive patients * No concurrent amifostine * No concurrent commercial agent or therapy intended to treat head and neck cancer * No other concurrent anticancer therapy