Phase 1b: - To determine the maximum tolerated dose (MTD) of oprozomib given orally, once daily, on 2 different schedules: 5 consecutive days every 14 days (bimonthly) or 2 consecutive days every 7 days (weekly) for a 14-day treatment cycle, both schedules given in combination with dexamethasone. - To evaluate safety and tolerability. Phase 2: - To estimate the overall response rate (ORR), defined as the proportion of subjects with the best overall response of stringent complete response (sCR), complete response (CR), near complete response (nCR), very good partial response (VGPR), and partial response (PR) as defined by the International Myeloma Working Group-Uniform Response Criteria (IMWG-URC) and modified European Group for Blood and Marrow Transplantation (EBMT) criteria. - To evaluate safety and tolerability.