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); patients with Gilbert?s syndrome may be included if total bilirubin =\< 3 x ULN or direct bilirubin =\< 1.5 x ULN * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x ULN if no liver metastases are present? =\< 5 x ULN if liver metastases are present * Alkaline phosphatase (ALP) =\< 5 x ULN * Serum amylase =\< grade 2 and asymptomatic; patients with grade 1 or 2 serum amylase at the beginning of the study must be confirmed to have no signs and/or symptoms suggesting pancreatitis or pancreatic injury (e.g., elevated P-amylase, abnormal imaging findings of pancreas, etc.) * Serum lipase =\< ULN * Creatinine OR creatinine clearance within normal limits \> 40 mL/min (calculated by Cockgraft-Gault) for patients with creatinine levels above ULN * Serum potassium, calcium (corrected for serum albumin), magnesium, phosphorus within normal limits with or without supplementation * CERITINIB INCLUSION CRITERIA: * Ability to understand a written informed consent document, and the willingness to sign it * 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 RECIST v1.1 * Documentation of absence of activating and targetable BRAF or NRAS point mutations * Presence of an oncogenic kinase fusion involving ALK, confirmed by assay by a CLIA-approved laboratory * Prior treatment with at least one 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 CTCAE v4.03 grade =\< 1 * Absolute neutrophil count \>= 1.5 x 10\^9/L * Platelets \>= 75 x 10\^9/L * Hemoglobin \>= 8 g/dL (transfusions are allowed) * Total bilirubin =\< 1.5 x upper limit of normal (ULN); patients with Gilbert?s syndrome may be included if total bilirubin =\< 3 x ULN and direct bilirubin =\< 1.5 x ULN * AST (SGOT) and ALT (SGPT) =\< 3 x ULN if no liver metastases are present? =\< 5 x ULN if liver metastases are present * Alkaline phosphatase (ALP) =\< 5 x ULN * Serum amylase =\< 2 x ULN * Serum lipase =\< ULN * Fasting plasma glucose =\< 175 mg/dL (=\< 9.8 mmol/L) * Creatinine OR creatinine clearance \< 1.5 mg/dL \>= 30 mL/min (calculated by Cockgraft-Gault) for patients with creatinine levels above ULN * Serum potassium, calcium (corrected for serum albumin), magnesium, phosphorus within normal limits with or without supplementation * REGORAFENIB INCLUSION CRITERIA: * Ability to understand a written informed consent document, and the willingness to sign it * 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 RECIST v1.1 * Documentation of absence of activating and targetable BRAF or NRAS point mutations * Presence of an oncogenic kinase fusion involving BRAF or RET, confirmed by assay by a CLIA-approved laboratory * Prior treatment with at least one 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 CTCAE v4.03 grade =\< 1 * Absolute neutrophil count \>= 1,500/mm\^3 * Platelets \>= 100,000/mm\^3 * Hemoglobin \>= 9 g/dL * Total bilirubin =\< 1.5 x upper limit of normal (ULN); patients with Gilbert?s syndrome may be included if total bilirubin =\< 3 x ULN or direct bilirubin =\< 1.5 x ULN * AST (SGOT) and ALT (SGPT) =\< 2.5 x ULN if no liver metastases are present? =\< 5 x ULN if liver metastases are present * Alkaline phosphatase (ALP) =\< 2.5 x ULN if no liver metastases are present; =\< 5 x ULN if bone or liver metastases are present * Creatinine OR creatinine clearance =\< 1.5 x ULN; \> 40 mL/min (calculated by Cockgraft-Gault) for patients with creatinine levels above ULN * Serum potassium, calcium (corrected for serum albumin), magnesium, phosphorus within normal limits with or without supplementation * International normalized ratio (INR) and partial thromboplastin time (PTT) =\< 1.5 x ULN (patients who are prophylactically treated with an agent such as warfarin or heparin will be allowed to participate, provided that no prior evidence of underlying abnormality in coagulation parameters exists; close monitoring of at least weekly evaluations will be performed until INR/PTT is stable based on a measurement that is predose as defined by the local standard of care) * ENTRECTINIB INCLUSION CRITERIA: * Ability to understand a written informed consent document, and the willingness to sign it * ECOG performance status 0-2 * Histologically or cytologically confirmed invasive melanoma * Unresectable stage III or stage IV melanoma by clinical or radiographic criteria * Measurable disease by RECIST v1.1 * Patients with central nervous system (CNS) involvement, including leptomeningeal carcinomatosis, which is either asymptomatic or previously-treated and controlled, are allowed; the use of seizure prophylaxis is allowed as long as patients are taking non enzyme-inducing anti-epileptic drugs (non-EIAEDs); if patients were previously on EIAEDs and these have been discontinued, they must have been discontinued for at least 2 weeks prior to the start of entrectinib treatment; if patients require an anti-epileptic medication, a CYP3A4 non-EIAED can be used such as levetiracetam, valproic acid, gabapentin, topiramate, or lacosamide; moderate inducers of CYP450, such as dexamethasone or other glucocorticoids, may be used at the discretion of the investigator; patients requiring steroids must be at a stable or decreasing doses for at least 2 weeks prior to the start of entrectinib treatment * Documentation of absence of activating and targetable BRAF or NRAS point mutations * Presence of an oncogenic kinase fusion involving ROS1 or NTRK1/2/3, confirmed by assay by a CLIA-approved laboratory * Prior treatment with at least one 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 CTCAE v4.03 grade =\< 1 * Absolute neutrophil count \>= 1,000/mm\^3 * Platelets \>= 75,000/mcL * Hemoglobin \>= 8 g/dL (transfusions are allowed) * Total bilirubin =\< 1.5 x upper limit of normal (ULN); patients with Gilbert?s syndrome may be included if total bilirubin =\< 3 x ULN or direct bilirubin =\< 1.5 x ULN * AST (SGOT) and ALT (SGPT) =\< 3.0 x ULN if no liver metastases are present? =\< 5 x ULN if liver metastases are present * Creatinine OR creatinine clearance within normal limits; \> 40 mL/min (calculated by Cockgraft-Gault) for patients with creatinine levels above ULN Exclusion Criteria: * CAPMATINIB EXCLUSION CRITERIA: Uveal melanoma * CAPMATINIB EXCLUSION CRITERIA: Current participation in another therapeutic clinical trial * CAPMATINIB EXCLUSION CRITERIA: Inability to swallow intact tablets or capsules * CAPMATINIB EXCLUSION CRITERIA: Previously identified allergy or hypersensitivity to components of capmatinib formulation (crospovidone, mannitol, microcrystalline cellulose, povidone, sodium lauryl sulfate, magnesium stearate, colloidal silicon dioxide, and various coating premixes) * CAPMATINIB EXCLUSION CRITERIA: Diagnosis of concurrent malignancy or previous malignancy within 3 years before study drug administration (exceptions are superficial skin cancers, or any in situ cancers deemed surgically resected, cured and not requiring systemic therapy, and indolent malignancies that currently do not require treatment) * CAPMATINIB EXCLUSION CRITERIA: Prior treatment with the following antineoplastic therapies within the following time frame: * Any prior treatment with capmatinib, crizotinib, or any other cMET or hepatocyte growth factor (HGF) inhibitor * Thoracic radiotherapy to lung fields =\< 4 weeks prior to starting capmatinib; for all other anatomic sites (including radiotherapy to thoracic vertebrae and ribs), radiotherapy =\< 2 weeks prior to starting capmatinib; palliative radiotherapy for bone lesions =\< 2 weeks prior to starting capmatinib is allowed * Receipt of any anticancer or investigational agent within 4 weeks or =\< 5 half-lives of the agent (whichever is longer) prior to the first dose of capmatinib; if previous treatment is a monoclonal antibody, then the treatment must be discontinued at least 4 weeks before the first dose of capmatinib * CAPMATINIB EXCLUSION CRITERIA: Major surgery (e.g., intrathoracic, intraabdominal or intrapelvic) within 4 weeks prior (2 weeks for resection of brain metastases) to starting capmatinib; video-assisted thoracic surgery (VATS) and mediastinoscopy will not be counted as major surgery and patients can be enrolled in the study \>= 1 week after the procedure * CAPMATINIB EXCLUSION CRITERIA: Patients receiving treatment with medications that meet one of the following criteria and that cannot be discontinued at least 1 week prior to the start of capmatinib treatment and for the duration of the study: * Strong and moderate inhibitors of CYP3A4 * Strong inducers of CYP3A4 * Proton pump inhibitors (PPI) * CAPMATINIB EXCLUSION CRITERIA: Patients on unstable or increasing doses of corticosteroids; if patients are on corticosteroids for endocrine deficiencies or tumor-associated symptoms other than CNS related, dose must have been stabilized or decreasing for at least 5 days before first dose of capmatinib * CAPMATINIB EXCLUSION CRITERIA: Presence or history of carcinomatous meningitis * CAPMATINIB EXCLUSION CRITERIA: Known symptomatic brain metastases requiring increasing doses of steroid to manage CNS symptoms within 2 weeks prior to study entry * Patients with asymptomatic brain metastases may be enrolled at the discretion of the sponsor as long as the patient is stable and has not required increasing dose of steroids to manage CNS symptoms for at least 2 weeks prior to study enrollment * Patients requiring seizure prophylaxis must be taking non-enzyme-inducing anti-epileptic drugs (non-EIAED); if patients were previously on EIAEDs and these have been discontinued, they must be discontinued for at least 1 weeks prior to capmatinib administration; if patients re