Ubiquitin-protein ligases x IKZF1 x IKZF3

This phase II trial studies how well mezigdomide/carfilzomib/dexamethasone (MeziKD) works in treating patients with multiple myeloma (MM) that has come back after a period of improvement (relapsed) or that does not respond to treatment (refractory) and have tumors from myeloma cells outside the bone marrow in the soft tissues or organs of the body (extramedullary disease [EMD]). Mezigdomide blocks important processes in myeloma cells and may lead to modulation of the immune system, including activation of T-lymphocytes, and downregulation of the activity of other proteins, some of which play key roles in the proliferation of certain cancer cell types. Carfilzomib may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. Dexamethasone is a type of corticosteroid and is used to kill myeloma cells. It is used with other drugs to treat multiple myeloma. Giving MeziKD may kill more cancer cells in patients with relapsed/refractory multiple myeloma (RRMM) with EMD.