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 (Hg…