This phase II trial studies how well dexamethasone, elotuzumab, pomalidomide work in treating patients with multiple myeloma that has not responded to previous treatment. Drugs used in chemotherapy, such as dexamethasone, 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. Immunotherapy with monoclonal antibodies, such as elotuzumab, may help the body?s immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. Pomalidomide may stop the growth of multiple myeloma by blocking the growth of new blood vessels necessary for tumor growth. Giving dexamethasone, elotuzumab, pomalidomide may work better in treating patients with multiple myeloma.