RATIONALE: Pomalidomide and bortezomib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Bortezomib may also stop the growth of tumor cells by blocking blood flow to the tumor. Drugs used in chemotherapy, such as dexamethasone, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Giving pomalidomide and bortezomib together with dexamethasone may kill more tumor cells. PURPOSE: This phase I/II trial is studying the side effects and best dose of bortezomib when given together with pomalidomide and dexamethasone and to see how well it works in treating patients with relapsed or refractory multiple myeloma.