Patients receive melphalan IV over 30 minutes on days -2 and -1. Half of the stored PBSCs and/or bone marrow is reinfused on day 0. Patients receive sargramostim (GM-CSF) daily beginning on day 0 and continuing until blood counts recover. Patients with primary systemic amyloidosis who are not responding to or are unable to tolerate treatment do not proceed to the second course of therapy.