This randomized phase I trial studies the side effects and best way to give ipilimumab with or without dabrafenib and/or trametinib in treating patients with melanoma that is metastatic or cannot be removed by surgery. Monoclonal antibodies, such as ipilimumab, can block tumor growth in different ways. Some block the ability of tumor to grow and spread. Others find tumor cells and help kill them or carry tumor-killing substances to them. Dabrafenib and trametinib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. It is not yet known whether ipilimumab works better with or without dabrafenib and/or trametinib in treating melanoma.