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.

OBJECTIVES: I. Determine the effectiveness of interferon alfa-2b maintenance following high dose melphalan chemotherapy for patients with advanced multiple myeloma. II. Determine the response rate to high dose dexamethasone therapy using sequential noncrossresistant chemotherapies for patients with advanced multiple myeloma.

OUTLINE: Patients receive high dose dexamethasone on days 1-4, 9-12, and 17-20, followed by 4 weeks rest. Cyclophosphamide (CTX) is administered intravenously in combination with mesna following dexamethasone therapy. Sargramostim (GM-CSF) is initiated subcutaneously 1 day later and is continued for 10 days to support stem cell collections, which begin 10-14 days after CTX induction. Following 4 weeks of rest, melphalan (L-PAM) is administered over 1 hour. Stem cell rescue is begun 48 hours after L-PAM therapy. Three to 4 months after the first L-PAM course, a second L-PAM and stem cell rescue is undertaken. Interferon alfa-2b (IFN-A) maintenance is administered 3 times per week following bone marrow recovery from the first or second L-PAM courses. Patients achieving complete remission following the first course of L-PAM may proceed directly to IFN-A maintenance. Patients achieving greater than grade 3 nonhematologic toxicity or not achieving an absolute neutrophil count of greater than 1,000/mm3 by day 21 posttransplant are not eligible for dose escalation.

PROJECTED ACCRUAL: A minimum of 30 patients will be enrolled.

DISEASE CHARACTERISTICS: See General Eligibility Criteria

PATIENT CHARACTERISTICS: Age: 19 to 64 Performance Status: Zubrod 0-3 Hematopoietic: Not specified Hepatic: Bilirubin less than 2 mg/dL SGOT and SGPT less than 3 times normal Alkaline phosphatase less than 3 times normal Renal: Creatinine clearance at least 60 mL/min Cardiovascular: Cardiac ejection fraction at least 50% Pulmonary: No history of severe chronic obstructive lung disease No history of recurrent pulmonary emboli Other: Not pregnant or nursing Effective contraception should be practiced by fertile patients No history of diabetes mellitus complicated by ketoacidosis No history of depression or psychosis No history of autoimmune disorders No concurrent thyroid disorders unable to be maintained on replacement therapy No prior hypersensitivity to interferon alfa-2b

PRIOR CONCURRENT THERAPY: Biologic therapy: Not specified Chemotherapy: No more than 12 months of prior alkylator therapy Endocrine Therapy: Not specified Radiotherapy: Not specified Surgery: Not specified