Patients receive 131 I-MIBG IV over 120 minutes on day -21; melphalan IV on days -7 to -5; carboplatin and etoposide IV continuously over 96 hours on days -7 to -4; autologous hematopoietic stem cell transplantation IV over 15-30 minutes on day 0; and filgrastim (G-CSF) subcutaneously or IV starting on day 0 and continuing until blood counts recover. Radiotherapy is administered to the primary tumor site and metastatic sites twice daily for 7 consecutive days within 6 weeks of transplantation or once blood counts have recovered.