This randomized phase II trial studies how well giving bortezomib with or without combination chemotherapy works as consolidation therapy in patients with newly diagnosed multiple myeloma who have completed stem cell transplant. Bortezomib may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. Drugs used in chemotherapy, such as cyclophosphamide, dexamethasone, and lenalidomide, work in different ways to stop the growth of cancer cells, either by killing the cells or by stopping them from dividing. It is not yet known whether giving bortezomib is more effective with or without combination chemotherapy in the post transplant setting.