A second transplant may be considered, preferably between 3 and 6 months after the first transplant. The preferred regimen for the second transplant is melphalan alone or melphalan plus TBI as described above. The alternative regimens for the second dose therapy are melphalan alone or melphalan plus cyclophosphamide. For patients receiving melphalan alone, melphalan is administered in one dose on day -1 at least 12 hours before stem cell infusion. Hematopoietic stem cells are reinfused on day 0 for both alternative regimens.