Capmatinib, Ceritinib, Regorafenib, or Entrectinib in Treating Patients With BRAF/NRAS Wild-Type Stage III-IV Melanoma

Inclusion Criteria: * CAPMATINIB INCLUSION CRITERIA: * Ability to understand a written informed consent document, and the willingness to sign it * Eastern Cooperative Oncology Group (ECOG) performance status 0-1 * Life expectancy \>= 12 weeks * Histologically or cytologically confirmed invasive melanoma * Unresectable stage III or stage IV melanoma by clinical or radiographic criteria * Measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) version (v)1.1 * Documentation of absence of activating and targetable BRAF or NRAS point mutations * Presence of an oncogenic kinase fusion involving MET, confirmed by assay by a Clinical Laboratory Improvement Act (CLIA)-approved laboratory * Prior treatment with at least one Food and Drug Administration (FDA)-approved drug for unresectable/metastatic melanoma; patients who are treatment-naive but who refuse available standard options and prefer to enroll on this study as their first line of treatment after a thorough informed consent process will be eligible at the discretion of the treating physician * Resolution of all acute toxic effects (excluding alopecia) of prior radiotherapy, chemotherapy or surgical procedures to Common Terminology Criteria for Adverse Events (CTCAE) v4.03 grade =\< 1 * Absolute neutrophil count \>= 1,500/mm\^3 * Platelets \>= 75,000/ microliters (mcL) * Hemoglobin \>= 9 g/dL (transfusions are allowed) * Total bilirubin =\< 1.5 x upper limit of normal (ULN); pa…