Testing Sunitinib as Potentially Targeted Treatment in Cancers With cKIT Genetic Changes (MATCH - Subprotocol V)

Inclusion Criteria:

* Patients must have met applicable eligibility criteria in the Master MATCH Protocol EAY131/ NCI-2015-00054 prior to registration to treatment subprotocol
* Patients must fulfill all eligibility criteria of MATCH Master Protocol at the time of registration to treatment step (Step 1, 3, 5, 7)
* Patients must have a somatic cKIT mutation in exon 9, 11, 13 or 14, excluding exon 17 or 18 mutations, activating PDGFRA or PDGFRB variants and fusions, or another aberration, as identified via the MATCH Master Protocol

  * Actionable mutations of interest (aMOIs)for information on the inclusion and exclusion mutations, along with the corresponding levels of evidence (LOE)
* Total bilirubin must be within normal institutional limits
* Creatinine must be within normal institutional limits. OR Creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal
* Serum calcium must be =\< 12.0 mg/dL
* Patients must have an electrocardiogram (ECG) within 8 weeks prior to treatment assignment and must have no clinically important abnormalities in rhythm, conduction or morphology of resting ECG (e.g. complete left bundle branch block, third degree heart block)
* Patients with known left ventricular dysfunction must have ECHO or a nuclear study (multigated acquisition scan \[MUGA\] or first pass) within 4 weeks prior to registration to treatment and must not have left ventricular ejection fraction (LVEF) \< institutional lower limit of normal (LLN). If the LLN is not defined at a site, the LVEF must be \> 50% for the patient to be eligible.

  * The following groups of patients are eligible provided they have New York Heart Association class II cardiac function on baseline ECHO/nuclear study:

    * Patients with a history of class II heart failure who are asymptomatic on treatment
    * Patients with prior anthracycline exposure
    * Patients who have received central thoracic radiation that included the heart in the radiotherapy port NOTE: Pre-treatment LVEF determination in patients without known left ventricular dysfunction (or per Section 2.1.5.1) is NOT otherwise required
* Patients with any of the following conditions are excluded:

  * Serious or non-healing wound, ulcer, or bone fracture
  * History of abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within 28 days of treatment
  * Any history of cerebrovascular accident (CVA) or transient ischemic attack within 12 months prior to study entry
  * History of myocardial infarction, cardiac arrhythmia, stable/unstable angina, symptomatic congestive heart failure, or coronary/peripheral artery bypass graft or stenting within 12 months prior to study entry
  * History of pulmonary embolism within the past 12 months
* Patients must not have known hypersensitivity or excess toxicity from sunitinib or compounds of similar chemical composition or biologic effect. This list includes, but is not limited to, patients with significant cardiac or hepatic toxicity from multikinase inhibitors with similar kinase inhibitory profiles (sorafenib, regorafenib, pazopanib)

  * Questions regarding a significant intolerance to a prior therapy should be directed to the sub-protocol principal investigator (PI)
* Patients must not have had prior therapy with sunitinib
* Patients must not have planned ongoing administration of STRONG and MODERATE CYP3A4 inhibitors or inducers. The reference list of cytochrome p450 (CYP) isozymes and classification of strong, moderate, and weak interactions is available through the FDA website

  * Strong CYP3A4 inhibitors are not permitted within 7 days before dosing and should be avoided throughout the study
  * Strong CYP3A4 inducers are not permitted within 12 days before dosing and should be avoided throughout the study
* Patients must not have gastrointestinal stromal tumor (GIST), renal cell carcinoma, or pancreatic neuroendocrine tumor
* Patients must not have a National Cancer Institute Common Terminology Criteria for Adverse Events (NCI CTCAE) version 4 grade 3 hemorrhage within 4 weeks of starting study treatment
* Patients must not have hypertension that cannot be controlled by medications (\> 140/90 mmHg despite optimal medical therapy)
* Patients must not have pre-existing thyroid abnormality with thyroid function that cannot be maintained in the normal range with medication
* Participants may not have a major surgical procedure, open biopsy, or significant traumatic injury within 28 days prior to starting sunitinib
* Patients with known brain metastases should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events
* Patients who require therapeutic doses of coumarin derivative anticoagulants such as warfarin are excluded, although doses up to 2 mg daily are permitted for prophylaxis of thrombosis NOTE: Low molecular weight heparin is permitted provided that the patient's prothrombin time (PT) international normalized ratio (INR) is \< 1.5