OUTLINE: This is a randomized, multicenter study. Patients are stratified according to prior complete remission to first-line treatment (yes vs no), primary site of disease (testicular vs retroperitoneal vs mediastinal), and lung metastases at study entry (yes vs no). Autologous bone marrow and peripheral blood stem cells (PBSC) are harvested. Part I (salvage): Patients are assigned to regimen A if they previously received vinblastine as part of a first-line treatment, such as cisplatin, vinblastine, and bleomycin (PVB) or cisplatin, cyclophosphamide, doxorubicin, vinblastine, and bleomycin (CISCA VB). Patients are assigned to regimen B if they previously received etoposide (VP-16) as part of a first-line treatment, such as bleomycin, VP-16, and cisplatin (BEP). Regimen A: Patients receive cisplatin IV over 2 hours, VP-16 IV over 2 hours, and ifosfamide IV over 1 hour on days 1-5 (PEI). Regimen B: Patients receive cisplatin and etoposide as in regimen A and vinblastine IV on days 1 and 2 (VeIP). Treatment on both regimens continues every 3 weeks for 2 courses. Patients with refractory disease at day 43 are taken off study. Part II: Patients are randomized to 1 of 2 treatment arms. Arm I: Patients receive 2 additional courses of PEI or VeIP. Arm II: Patients receive 1 additional course of PEI or VeIP, followed by 1 course of high-dose carboplatin IV over 2 hours, VP-16 IV over 2 hours, and cyclophosphamide IV over 1 hour on days 1-4. Autologous bone marrow and/or PBSC are reinfused on day 7 of the fourth course for patients on both arms. Patients on both arms with residual disease after the fourth course may undergo surgery.