Dovitinib Lactate in Treating Patients With Pancreatic Neuroendocrine Tumors

Inclusion Criteria: * Histologic diagnosis of a well- to moderately differentiated PNET (low-intermediate grade); NOTE: pathology report should state one of the following: low-grade, intermediate grade, moderately- or well-differentiated NET, pancreatic NET (or neuroendocrine carcinoma of the pancreas); patients who have tumors with a Ki67 of 20 % - 30 % are eligible if the pathologist determines the tumor has the appearance of a well- to moderately differentiated neuroendocrine tumor * Documented radiological evidence for disease progression (measurable or nonmeasurable) =\< 12 months prior to enrollment; NOTE: if the patient has had previous radiation to the marker lesion(s), there must be evidence of progression since the radiation; at least one measurable lesion as per Response Evaluation Criteria In Solid Tumors (RECIST) * Disease that is currently not amenable to surgery, radiation, or combined modality therapy with curative intent * COHORT 2 ONLY: Prior treatment with a VEGF inhibitor (e.g. sunitinib, bevacizumab, sorafenib or other dedicated VEGF inhibitor) * Recovered from adverse events (to grade 1 or less toxicity according to Common Terminology Criteria for Adverse Events \[CTCAE\] 4.0) due to agents administered previously; NOTE: chemotherapy-induced alopecia and grade 2 neuropathy are acceptable * Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 * Absolute neutrophil count (ANC) \>= 1.5 x 10\^9/L * Platelets \>= 100 x 10\^9/L * Hemoglobin (Hgb) \> 9 g/dL * Serum total bilirubin =\< 1.5 x upper limit of normal (ULN) * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 3.0 x ULN * Serum creatinine =\< 1.5 x ULN * Provide informed written consent * Negative pregnancy test done =\< 14 days prior to registration, for women of childbearing potential only * Willing to return to an Academic and Community Cancer Research United (ACCRU) enrolling institution for follow-up (i.e., active monitoring, which includes active treatment and observation) * Willing to provide mandatory blood samples for correlative research purposes Exclusion Criteria: * Clinical evidence for brain metastases (including carcinomatous meningitis) at baseline (may require imaging assessment, e.g. computed tomography \[CT\] or magnetic resonance imaging \[MRI\], for certain patient population), with the exception of those subjects who have previously-treated central nervous system (CNS) metastases (surgery ± radiotherapy, radiosurgery, or gamma knife) and who meet both of the following criteria: a) are asymptomatic and b) have had no requirement for steroids or enzyme- inducing anticonvulsants within 6 months prior to study entry * Participated in a prior anticancer investigational study =\< 30 days prior to enrollment, or =\< 5 half-lives of the anticancer investigational product, whichever is longer (treatment with somatostatin analogue \[SSTa\] while on dovitinib is allowed provided patient's tumor has progressed on therapy prior to initiating dovitinib treatment) * COHORT 1 ONLY: Prior treatment with a VEGF inhibitor (e.g. sunitinib, bevacizumab, sorafenib or other dedicated VEGF inhibitor) * Liver-directed therapy (hepatic artery chemoembolization \[HACE\], hepatic artery embolization \[HAE\], selective internal radiation therapy \[SIRT\]) or peptide receptor radionuclide therapy (PRRT) =\< 56 days of first dose of study drug * Another primary malignancy =\< 3 years prior to starting study treatment, with the exception of adequately treated basal cell carcinoma, squamous cell carcinoma or other non-melanomatous skin cancer, or in-situ carcinoma of the uterine cervix * Received the last administration of an anticancer targeted small molecule therapy (e.g. sunitinib, sorafenib, pazopanib, axitinib, everolimus, temsirolimus, ridaforolimus) =\< 14 days prior to study registration or have not recovered from the side effects of such therapy * Received the last administration of an anticancer monoclonal antibody, immunotherapy, hormonal therapy, or chemotherapy (except nitrosoureas and mitomycin-C) =\< 28 days prior to study registration or who have not recovered from the side effects of such therapy * Received the last administration of nitrosourea or mitomycin-C =\< 42 days prior to study registration, or who have not recovered from the side effects of such therapy * Radiotherapy (external beam or CyberKnife) =\< 28 days prior to starting study drug, or =\< 14 days prior to study registration in the case of localized radiotherapy (e.g. for analgesic purpose or for lytic lesions at risk of fracture), or who have not recovered from radiotherapy toxicities * Undergone major surgery (e.g. intra-thoracic, intra-abdominal or intra-pelvic), open biopsy or significant traumatic injury =\< 28 days prior to study registration, or had minor procedures, percutaneous biopsies or placement of vascular access device =\< 7 days prior to study registration, or have not recovered from side effects of such procedure or injury * History of pulmonary embolism (PE), or untreated deep venous thrombosis (DVT) =\< 180 days * Impaired cardiac function or clinically significant cardiac diseases, including any of the following: * History or presence of serious uncontrolled ventricular arrhythmias * Clinically significant resting bradycardia * Ongoing cardiac dysrhythmias, atrial fibrillation, or prolongation of corrected QTc interval to \> 480 msec • \* Left ventricular ejection fraction (LVEF) assessed by 2-dimensional (2-D) echocardiogram (ECHO) \< 50% or lower limit of normal (whichever is the higher), or 2-D multiple gated acquisition scan (MUGA) \< 45% or lower limit of normal (whichever is the higher) * Any of the following =\< 180 days prior to starting study drug: myocardial infarction (MI), severe/unstable angina, coronary artery bypass graft (CABG), congestive heart failure (CHF), cerebrovascular accident (CVA), transient ischemic attack (TIA) * Uncontrolled hypertension defined by a systolic blood pressure (SBP) \>= 160 mm Hg and/or diastolic (D)BP \>= 100 mm Hg, with or without anti-hypertensive medication(s); initiation or adjustment of antihypertensive medication(s) is allowed prior to study entry * Impairment of gastrointestinal (GI) function or GI disease that may significantly alter the absorption of dovitinib (e.g. ulcerative diseases, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome, or gastric or small bowel resection) * History of abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within 28 days prior to registration * No clinically significant gastrointestinal abnormalities that may increase the risk of gastrointestinal bleeding within 28 days prior to registration including, but not limited to: * Active peptic ulcer * Known endoluminal metastatic lesion(s) with history of bleeding * Active inflammatory bowel disease (e.g. ulcerative colitis, Crohn's Disease), or other gastrointestinal conditions with increased risk of perforation * No evidence of active bleeding, bleeding diathesis, or hemoptysis (\>= ½ teaspoon of red blood) within 8 weeks of registration * Immunocompromised patients and patients known to be human immunodeficiency virus (HIV) positive and currently receiving antiretroviral therapy (HIV testing not required); NOTE: patients known to be HIV positive, but without clinical evidence of an immunocompromised state (cluster of differentiation \[CD\]4 \> 200, viral load undetectable, on antiretroviral therapy), are eligible for this trial * Currently receiving antiplatelet therapy of prasugrel or clopidogrel, or full dose anticoagulation treatment with therapeutic doses of warfarin; Note: treatment with low doses of warfarin (e.g., =\< 2 mg/day ) for line patency allowed; also, low molecular weight heparins, fondaparinux, antiaggregation agents (e.g., eptifibatide, epoprostenol, dipyridamole) or locally accepted low doses of acetylsalicylic acid (up to 100 mg daily) may be administered concomitantly with dovitinib with caution * Other concurrent severe and/or uncontrolled concomitant medical conditions (e.g. active or uncontrolled infection, uncontrolled diabetes) that could cause unacceptable safety risks or compromise compliance with the protocol * Any of the following: * Pregnant women * Nursing women * Men or women of childbearing potential who are unwilling to employ adequate contraception * Pregnant or nursing (lactating) women, where pregnancy is defined as the state of a female after conception and until the termination of gestation, confirmed by a positive human chorionic gonadotropin (hCG) laboratory test * Women of child-bearing potential, defined as all women physiologically capable of becoming pregnant, unless they are using highly effective methods of contraception (defined below); highly effective contraception must be used by both sexes (female patients and their male partners) during study treatment and for 30 days after the last dose of study medication; highly effective contraception methods include: * Total abstinence (when this is in line with the preferred and usual lifestyle of the subject); periodic abstinence (e.g., calendar, ovulation, symptothermal, post-ovulation methods) and withdrawal are not acceptable methods of contraception * Female sterilization (have had surgical bilateral oophorectomy with or without hysterectomy) or tubal ligation at least six weeks before taking study treatment; in case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment * Combination of the following: * Placement of an intrauterine device (IUD) or intrauterine system (IUS) * Barrier methods of contraception: condom or occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/vaginal suppository * Oral, implantable, or injectable hormone contraceptives are not considered effective for this study * Women of child-bearing potential (sexually mature women) who have not undergone a hysterectomy or who have not been naturally postmenopausal for at least 12 consecutive months (i.e., who has had menses any time in the preceding 12 consecutive months), must have a negative serum pregnancy test =\< 14 days prior to starting study drug * Fertile males not willing to use contraception; fertile males must use condom with spermicide; highly effective contraception, as defined above, must be used by both sexes (male patients and their female partners) during study treatment and for 90 days after the last dose of study medication and should not father a child in this period; a condom is required to be used also by vasectomized men * Unwilling or unable to comply with the protocol * Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens * Currently receiving any other investigational agent which would be considered as a treatment for the primary neoplasm