This phase II trial studies the effect of isatuximab, carfilzomib, pomalidomide, and dexamethasone in treating patients with multiple myeloma that has come back (relapsed) or does not respond to treatment (refractory). Isatuximab is a monoclonal antibody that may interfere with the ability of cancer cells to grow and spread. Carfilzomib may stop the growth of cancer cells by blocking some of the proteins needed for cell growth. Chemotherapy drugs, such as pomalidomide, work in different ways to stop the growth of cancer cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Anti-inflammatory drugs, such as dexamethasone lower the body's immune response and are used with other drugs in the treatment of some types of cancer. Giving isatuximab, carfilzomib, pomalidomide, and dexamethasone may kill more cancer cells.