Vemurafenib With Sorafenib Tosylate or Crizotinib in Treating Patients With Advanced Malignancies With BRAF Mutations

Inclusion Criteria: * Patients with advanced or metastatic cancers and BRAF mutations that are refractory to standard therapy, relapsed after standard therapy, or who have no standard therapy available that improves survival by at least three months; patients with BRAF mutation in cell free deoxyribonucleic acid (DNA) (tested in Clinical Laboratory Improvement Amendments \[CLIA\] lab) are also eligible * Patients must be \>= 3 weeks beyond treatment with a cytotoxic chemotherapy regimen, or therapeutic radiation, or major surgery; patients may have received palliative localized radiation immediately before or during treatment provided that radiation is not delivered to the only site of disease being treated under this protocol; for biologic/targeted agents patients must be \>= 5 half-lives or \>= 3 weeks from the last dose (whichever comes first); patients previously treated with vemurafenib monotherapy do not have to stop medication before they start on the protocol * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Absolute neutrophil count (ANC) \>= 1,000/mL * Platelets \>= 75,000/mL * Creatinine =\< 2 X upper limit of normal (ULN) * Total bilirubin =\< 2 X ULN (exceptions may apply to benign non-malignant indirect hyperbilirubinemia such as Gilbert syndrome) * Alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) and/or aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) =\< 5 X ULN * Exception for patients with liver metastasis: total bilirubin =\< 3 x ULN; ALT (SGPT) =\< 8 X ULN * Dermatology evaluation with excision of any suspicious lesions prior to initiation of therapy * Women of childbearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 30 days after the last dose * Women of childbearing potential must have a negative serum or urine pregnancy test within 2 weeks prior to initiation of therapy * Life expectancy \> 12 weeks in the opinion of the investigator * Patients must be able to understand and be willing to sign a written informed consent document * Patient must be able to swallow pills Exclusion Criteria: * Uncontrolled intercurrent illness, including, but not limited to, uncontrolled infection, uncontrolled asthma, need for hemodialysis, need for ventilatory support * Syndrome of congenital corrected QT interval (QTc) prolongation or QTc \> 500 msec * Patients with clinically significant cardiovascular disease: history of cerebrovascular accident (CVA) within 6 months, myocardial infarction or unstable angina within 6 months, or unstable angina pectoris * Pregnant or lactating women * History of hypersensitivity to vemurafenib * History of hypersensitivity to sorafenib for vemurafenib/sorafenib arm * History of hypersensitivity to crizotinib for vemurafenib/crizotinib arm * History of hypersensitivity to any component of the formulation * Patients unwilling or unable to sign informed consent document * Patients using any of the following medications: mesoridazine, dronedarone, thioridazine, ziprasidone, levomethadyl, and saquinavir for vemurafenib/sorafenib arm