This phase II trial studies the effectiveness of melphalan, peripheral stem cell transplantation, and interleukin-2 followed by interferon alfa in treating patients who have advanced multiple myeloma (MM). Drugs used in chemotherapy use different ways to stop tumor cells from dividing so they stop growing or die. Combining chemotherapy with peripheral stem cell transplantation may allow the doctor to give higher doses of chemotherapy drugs and kill more tumor cells. Interleukin-2 (IL2) may stimulate a person's white blood cells to kill multiple myeloma cells. Interferon alfa may interfere with the growth of cancer cells