Nivolumab With Trametinib and Dabrafenib, or Encorafenib and Binimetinib in Treating Patients With BRAF Mutated Metastatic or Unresectable Stage III-IV Melanoma

Inclusion Criteria: * Histologically confirmed metastatic melanoma (stage IV) or unresectable Stage III that have progressed on or after receiving prior PD-1 directed therapy; only patients with BRAF V600 mutated melanoma are eligible; please note that patients with brain metastasis are not required to have prior PD-1 * Prior therapies for metastatic melanoma are allowed, including chemo-, cytokine-, immuno, biological and vaccine-therapy as long as they did not include BRAFi, MEKi; patients who have progressed on or after receiving anti-PD-1therapy in the adjuvant setting are also allowed; prior ipilimumab and/or PD-1 directed therapy will be allowed with a washout period of 2 weeks and if all autoimmune adverse events have resolved to grade 1 (except endocrine abnormalities that require continuous replacement) * Evidence of evaluable disease * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * Patients with melanoma brain metastases are allowed regardless of prior PD-1 exposure. Subjects with brain metastases are eligible if: * Metastases have been treated and there is no magnetic resonance imaging (MRI) evidence of progression for 2 weeks after treatment is complete and within 14 days of the first dose of nivolumab administration; or * If they are untreated but asymptomatic; or * If they are untreated and symptomatic but symptoms are controlled on stable or decreasing doses of steroids for 14 days prior to drug administration; or * If they h…