Eligibility Criteria:
Criteria:
* Hemoglobin \>= 9 g/dL
* Histologically or cytologically confirmed squamous cell carcinoma of the head and neck:
* Recurrent and/or metastatic disease
* Measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as \>= 20 mm with conventional techniques OR as \>= 10 mm with spiral CT scan
* No known brain metastases
* Life expectancy \>= 2 months
* ECOG performance status (PS) 0-1 or Karnofsky PS 70-100% (for patients in cohort A)
* ECOG PS 2 or Karnofsky PS 60-70% (for patients in cohort B)
* WBC \>= 3,000/mm\^3
* Absolute neutrophil count \>= 1,500/mm\^3
* Platelet count \>= 100,000/mm\^3
* Calcium =\< 12.0 mg/dL
* Bilirubin normal
* AST and ALT =\< 2.5 times upper limit of normal
* Creatinine normal OR creatinine clearance \>= 60 mL/min
* QTc \< 500 msec
* No New York Heart Association class III or IV heart failure:
* Patients with the following are eligible provided they have New York Heart Association class II cardiac function on baseline ECHO/MUGA:
* History of class II heart failure and asymptomatic on treatment
* Prior anthracycline exposure
* Prior central thoracic radiation that included the heart in the radiotherapy port
* Not pregnant or nursing
* Negative pregnancy test
* Fertile patients must use effective contraception
* No history of allergic reactions to compounds of similar chemical or biological composition to sunitinib malate
* No history of serious ventricular arrhythmia (i.e., ventricular fibrillation or ventricular tachycardia \>= 3 beats in a row)
* No history of other significant ECG abnormalities
* No uncontrolled hypertension (defined as systolic blood pressure \[BP\] \>= 140 mm Hg or diastolic BP \>= 90 mm Hg)
* No condition resulting in an inability to take oral medication, including any of the following:
* Gastrointestinal tract disease resulting in an inability to take oral medication or a requirement for IV alimentation
* Active peptic ulcer disease
* No gastrostomy, jejunostomy, or other forms of enteral tube-feeding modalities
* No serious or nonhealing wound, ulcer, or bone fracture
* No abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within the past 28 days
* No cerebrovascular accident or transient ischemic attack within the past 12 months
* No myocardial infarction, cardiac arrhythmia, stable/unstable angina, symptomatic congestive heart failure, or coronary/peripheral artery bypass graft or stenting within the past 12 months
* No pulmonary embolism within the past 12 months
* No pre-existing uncontrolled thyroid abnormality (i.e., inability to maintain thyroid function within the normal range with medication)
* No uncontrolled intercurrent illness, including either of the following:
* Ongoing or active infection
* Psychiatric illness or social situation that would limit compliance with study requirement
* No more than two prior regimens for recurrent or metastatic disease:
* Prior chemotherapy as part of initial curative intent therapy (e.g., neoadjuvant, adjuvant, or concurrent chemoradiotherapy) is allowed and will not count as prior therapy for recurrent or metastatic disease
* At least 4 weeks since prior major surgery
* At least 4 weeks since prior chemotherapy (6 weeks for nitrosoureas or mitomycin C) and recovered
* At least 4 weeks since prior radiotherapy
* No prior treatment with any other antiangiogenic agent (e.g., bevacizumab, sorafenib, pazopanib, AZD2171, vatalanib, or VEGF Trap)
* No prior surgical procedure affecting absorption
* At least 7 days since prior and no concurrent use of CYP3A4 inhibitors, including any of the following:
* Azole antifungals (e.g., ketoconazole, itraconazole)
* Verapamil
* Clarithromycin
* HIV protease inhibitors (e.g., indinavir, saquinavir, ritonavir, atazanavir, nelfinavir)
* Erythromycin
* Delavirdine
* Diltiazem
* At least 12 days since prior and no concurrent CYP3A4 inducers, including any of the following:
* Rifampin
* Phenytoin
* Rifabutin
* Hypericum perforatum (St. John's wort)
* Carbamazepine
* Efavirenz
* Phenobarbital
* Tipranavir
* No concurrent therapeutic doses of coumarin-derivative anticoagulants (e.g., warfarin):
Concurrent dosing of =\< 2 mg of warfarin daily for prophylaxis of thrombosis is allowed; Concurrent low molecular weight heparin allowed provided prothrombin time INR is =\< 1.5
* No other concurrent investigational agents
* No concurrent agents with proarrhythmic potential, including any of the following:
* Terfenadine
* Quinidine
* Procainamide
* Disopyramide
* Sotalol
* Probucol
* Bepridil
* Haloperidol
* Risperidone
* Indapamide
* Flecainide
* No other concurrent anticancer agents or therapies
* No concurrent combination antiretroviral therapy for HIV-positive patients