Bortezomib may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. Drugs used in chemotherapy, such as dexamethasone, work in different ways to stop the growth of cancer cells, either by killing the cells or by stopping them from dividing. Lenalidomide may stimulate the immune system in different ways and stop cancer cells from growing. It is not yet known whether giving bortezomib together with dexamethasone is more effective with or without lenalidomide in treating multiple myeloma. This randomized phase III trial is studying bortezomib, dexamethasone, and lenalidomide to see how well they work compared with bortezomib and dexamethasone in treating patients with multiple myeloma previously treated with dexamethasone. (NCT00522392)