STEP CROSSOVER REGISTRATION (OPTIONAL): Patients must have documented disease progression while on CETIRI (Arm ) on this protocol; the Follow-up Tumor Assessment Form documenting disease progression must be submitted to Southwest Oncology Group (SWOG) prior to step crossover registration; registration to step crossover must be within days of discontinuation of CETIRI protocol treatment; patients going off treatment for any other reason are not eligible STEP CROSSOVER REGISTRATION (OPTIONAL): Patients must have a Zubrod performance status of or STEP CROSSOVER REGISTRATION (OPTIONAL): ANC >= ,/mcL within days prior to step crossover registration STEP CROSSOVER REGISTRATION (OPTIONAL): Platelets >= ,/mcL within days prior to step crossover registration STEP CROSSOVER REGISTRATION (OPTIONAL): Hemoglobin >= g/dL within days prior to step crossover registration STEP CROSSOVER REGISTRATION (OPTIONAL): AST and ALT both =< x institutional upper limit of normal (IULN) within days prior to step crossover registration STEP CROSSOVER REGISTRATION (OPTIONAL): Bilirubin =< . mg/dL within days prior to step crossover registration STEP CROSSOVER REGISTRATION (OPTIONAL): Calculated creatinine clearance > ml/min within days prior to step crossover registration STEP CROSSOVER REGISTRATION (OPTIONAL): Patients must have left ventricular ejection fraction (LVEF) >= % or >= lower limit of normal for the institution by echocardiogram within days prior to step crossover registration STEP CROSSOVER REGISTRATION (OPTIONAL): Patients must have a magnesium, potassium, calcium, sodium, bicarbonate, and chloride performed within days prior to step crossover registration Patients must have completed study drug on arm of A (i.e., last dose of nivolumab) =< months of re-registration to crossover dual agent therapy STEP (CROSSOVER ARM FOR PATIENTS WITH PROGRESSIVE DISEASE) The patient must have met all eligibility criteria (except as detailed below) at the time of crossover\r\n* RECIST defined measurable disease is not required\r\n* Only prior systemic therapy as part of step is allowed; patients who received allowed systemic therapy in the adjuvant setting prior to Step and were eligible for Step are not excluded from proceeding to Step if they meet other eligibility criteria\r\n* Malabsorption, swallowing difficulty, or other conditions that would interfere with the ingestion or absorption of dabrafenib or trametinib, or history of retinal vein occlusion are acceptable for patients crossing over to ipilimumab + nivolumab treatment\r\n* History of autoimmune disease, excluding interstitial lung disease or pneumonitis, is allowed in patients crossing over to dabrafenib/trametinib therapy\r\n* Patients crossing over from nivolumab/ipilimumab to dabrafenib/trametinib who underwent surgery or SRS to CNS metastases need not be off of steroids to start treatment \r\n* There is no restriction on serum LDH at crossover\r\n* Patients with a history of cardiovascular risks that developed during step of therapy should be discussed with study principal investigator (PI) at time of crossover REGISTRATION STEP : CROSSOVER STEP CROSSOVER REGISTRATION: Registration to Step Crossover must be within days of discontinuation of Arm protocol treatment; patients going off treatment for any other reason are not eligible CROSSOVER (STEP ) REGISTRATION: Patients must have progressed systemically on Arm of this study (pemetrexed monotherapy) CROSSOVER (STEP ) REGISTRATION: Patients must be registered to crossover (Step ) within days of discontinuing treatment on Arm of this study CROSSOVER (STEP ) REGISTRATION: ANC >= ,/ul CROSSOVER (STEP ) REGISTRATION: Platelet count >= ,/ul CROSSOVER (STEP ) REGISTRATION: Hemoglobin >= g/dL CROSSOVER (STEP ) REGISTRATION: Serum bilirubin =< X IULN CROSSOVER (STEP ) REGISTRATION: SGOT (AST) or SGPT (ALT) =< . x IULN CROSSOVER (STEP ) REGISTRATION: Male patients must have free and total testosterone level obtained within days prior to crossover (Step ) registration CROSSOVER (STEP ) REGISTRATION: Patients must have Zubrod performance status - within days prior to crossover (Step ) registration ELIGIBILITY CRITERIA FOR CROSSOVER REGISTRATION INCLUSION CRITERIA FOR CROSSOVER THERAPY CROSSOVER RE-REGISTRATION - INCLUSION CRITERIA Treatment cannot begin prior to re-registering to the crossover phase and will ideally begin =< days after registration for the crossover phase