 This pilot phase I trial studies the side effects and best dose of histone deacetylase HDAC inhibitor AR-42 AR-42 when given together with pomalidomide in treating patients with multiple myeloma that has returned after a period of improvement. HDAC inhibitor AR-42 may work to stop cancer growth by blocking an enzyme needed for cell growth. Pomalidomide is a drug used in chemotherapy that works to stop the growth of cancer cells by causing them to die. Giving HDAC inhibitor AR-42 together with pomalidomide may cause patients to respond better to treatment. 