Onalespib, Dabrafenib, and Trametinib in Treating Patients With BRAF-Mutant Melanoma or Solid Tumors That Are Metastatic or Cannot Be Removed by Surgery

Inclusion Criteria: * Patients must have histologically confirmed, BRAF-mutant (V600E/K) solid tumor (molecularly confirmed using Cobas assay or a comparable Food and Drug Administration \[FDA\]-approved assay) that is metastatic or unresectable, have received and tolerated prior BRAF or BRAF and MEK inhibitor (BRAF targeted) therapy at full dose or not previously received BRAF targeted therapy, and for which standard curative measures do not exist or are no longer effective * If test at Clinical Laboratory Improvement Act (CLIA)-certified laboratory (lab) used a non-FDA approved method, information about the assay must be provided; (FDA approved tests for BRAF V600 mutations in melanoma include: THxID BRAF Detection Kit and Cobas 4800 BRAF V600 Mutation Test) * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as \>= 20 mm with conventional techniques or as \>= 10 mm with spiral computed tomography (CT) scan, magnetic resonance imaging (MRI), or calipers by clinical exam * Prior therapy is allowed; patients may have received any number of prior lines of therapy, including treatment with a BRAF and/or MEK inhibitor * All prior anti-cancer treatment-related toxicities must be less than or equal to grade 1 according to the Common Terminology Criteria for Adverse Events version 5 (CTCAE version 5.0; National Ca…