Interferon Alfa Following Chemotherapy and Peripheral Stem Cell Transplantation in Treating Patients With Stage III or Stage IV Multiple Myeloma

RATIONALE: Drugs used in chemotherapy use different ways to stop tumor cells from dividing so they stop growing or die. Peripheral stem cell transplantation may allow the doctor to give higher doses of chemotherapy drugs and kill more tumor cells. Interferon alfa may interfere with the growth of cancer cells. PURPOSE: Phase II trial to determine the effectiveness of giving interferon alfa after chemotherapy and peripheral stem cell transplantation to patients who have stage III or stage IV multiple myeloma and who have been treated with high-dose melphalan.