Ipilimumab With or Without Dabrafenib, Trametinib, and/or Nivolumab in Treating Patients With Melanoma That Is Metastatic or Cannot Be Removed by Surgery

Inclusion Criteria: * Study participants must have histologically or cytologically confirmed unresectable or metastatic malignant melanoma * Study participants 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 * Study participants must have completed any prior treatment at least 3 weeks prior to treatment on this protocol; prior treatments may have included chemotherapy however may not have included BRAF or MEK inhibitors or immunotherapies (interleukin-2, ipilimumab, anti-programmed death \[PD\]1 antibodies etc.) excluding vaccine therapy; prior treatment with interferon in the adjuvant setting is allowed, though prior treatment with ipilimumab in the adjuvant setting is not; prior radiation therapy is allowed though must have included no more than 3000 centigray (cGy) to fields including substantial marrow * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Absolute neutrophil count (ANC) \>= 1.2 x 10\^9/L * Hemoglobin \>= 9 g/dL * Platelets \>= 100 x 10\^9/L * Albumin \>= 2.5 g/dL * Serum bilirubin =\< 1.5 x institutional upper limit of normal (ULN) except subjects with known Gilbert's syndrome * Aspartate aminotransf…