This randomized phase III trial studies lenalidomide and low-dose dexamethasone to see how well it works compared to lenalidomide and standard-dose dexamethasone, given with or without thalidomide, in treating patients with multiple myeloma. Biological therapies, such as lenalidomide, may stimulate the immune system in different ways and stop cancer cells from growing. Lenalidomide and thalidomide may also stop the growth of multiple myeloma by blocking blood flow to the cancer. 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. Giving lenalidomide, thalidomide, and dexamethasone together may kill more cancer cells.