Lenvatinib in Treating Patients With Metastatic or Advanced Pheochromocytoma or Paraganglioma That Cannot Be Removed by Surgery

Inclusion Criteria: * Histologically or cytologically confirmed malignant secretory or non-secretory pheochromocytoma or paraganglioma that is unresectable and deemed inappropriate for alternative local regional therapeutic approaches * Measurable disease * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1, or 2 * Life expectancy \> 24 weeks * Absolute neutrophil count (ANC) \>= 1500/mm\^3 * White blood cell (WBC) count \>= 3,000/mm\^3 * Platelet count \>= 100,000/mm\^3 * Hemoglobin \>= 9.0 g/dL (5.6 mmol/L); NOTE: transfusions are not allowed =\< 7 days prior to registration * Total bilirubin =\< 1.5 X upper limit of normal (ULN) (or total bilirubin =\< 3.0 X ULN with direct bilirubin =\< 1.5 X ULN in patients with well-documented Gilbert's Syndrome) * Aspartate transaminase (AST/serum glutamic oxaloacetic transaminase \[SGOT\]) =\< 2.5 X ULN * Creatinine =\< 1.5 x ULN * Urine protein/creatinine ratio =\< 1 OR 24-hour urine protein \< 1.5 gram * Negative pregnancy test done =\< 7 days prior to registration, for women of childbearing potential only * Blood pressure (BP) \< 150 mmHg (systolic) and \< 90 mmHg (diastolic); initiation or adjustment of BP medication is permitted prior to registration provided that the average of three BP readings at a visit prior to registration is \< 150/90 mmHg; NOTE: all patients with secretory pheochromocytoma or paraganglioma are REQUIRED to: 1) be evaluated in consultation by a hypertension specialist with specific experience in the management of hypertension in the setting of catecholamine-secreting tumors (usually an endocrinologist, nephrologist, or a cardiologist), and in the setting of hormone-associated hypertension) receive alpha- and beta-adrenergic blockade for at least 7-14 days prior to initiation of lenvatinib; the hypertension specialist of record for each patient should be committed to closely following the patient during the clinical study with evaluation by said specialist required at cycle 1 and 2 and thereafter on an as needed basis * Provide written informed consent * Willing to return to enrolling institution for follow-up (during the active monitoring phase of the study) * Ability to complete questionnaire(s) by themselves or with assistance Exclusion Criteria: * Any of the following: * Pregnant women * Nursing women * Men or women of childbearing potential who are unwilling to employ adequate contraception * Chemotherapy/systemic therapy, radiotherapy, immunotherapy or surgery =\< 21 days prior to registration or kinase inhibitor therapy =\< 14 days prior to registration or failure to recover from toxicities (to grade 1 or below) from treatment; NOTE: concurrent therapy with octreotide is allowed providing that tumor progression on this therapy has been demonstrated; concurrent therapy with bisphosphonates (e.g. zoledronic acid) or denosumab is also allowed; NOTE: an unlimited number of prior chemotherapeutic or biologic therapies for malignant pheochromocytoma or paraganglioma is permitted; this includes prior anti-angiogenesis therapies such as tyrosine kinase inhibitors * Active or 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 * Receiving any other investigational agent * Current use of warfarin for any reason; NOTE: if patient can be safely transitioned to another anticoagulant, they may be eligible provided other criteria are satisfied * Any of the following: * Correct QT (QTc) prolongation (defined as a QTc interval \>= 500 msecs) * Left ventricular ejection fraction (LVEF) \< institutional lower limits of normal (LLN) * Frequent ventricular ectopy * Evidence of ongoing myocardial ischemia * Receiving any medications or substances with risk of torsades de pointes; NOTE: medications or substances with known risk of torsades de pointes are prohibited; consult pharmacist for review if needed * Known active and/or untreated brain metastases * Known severe allergic or other prohibitive reactions to other tyrosine kinase inhibitors (TKI) * Prior treatment with lenvatinib * Any of the following conditions: * Active peptic ulcer disease * Inflammatory bowel disease (e.g., ulcerative colitis, Crohn's disease) or other gastrointestinal conditions which increase the risk of perforation * History of new abdominal fistula, gastrointestinal perforation or intra-abdominal abscess =\< 84 days prior to registration; NOTE: enrollment of patients with chronic/canalized fistulous tracts (present for \> 84 days) is allowed * Serious or non-healing wound, ulcer, or bone fracture * History of familial QTc prolongation syndrome * Any of the following conditions =\< 6 months prior to registration: * Cerebrovascular accident (CVA) or transient ischemic attack (TIA) * Serious or unstable cardiac arrhythmia * Admission for unstable angina or myocardial infarction * Cardiac angioplasty or stenting * Coronary artery bypass graft surgery * Pulmonary embolism, untreated deep venous thrombosis (DVT) or DVT which has been treated with therapeutic anticoagulation =\< 30 days * Arterial thrombosis * Symptomatic peripheral vascular disease * Other active malignancy =\< 2 years prior to registration; EXCEPTIONS: non-melanotic skin cancer or carcinoma-in-situ of the cervix; NOTE: if there is a history of prior malignancy, they must not be receiving other specific treatment for their cancer; NOTE: adjuvant anti-estrogen/hormonal therapy for breast cancer is allowed