High-Dose Chemotherapy and Stem Cell Transplant in Treating Patients With Metastatic Germ Cell Tumors That Have Not Responded to First-Line Therapy

DISEASE CHARACTERISTICS: * Histologically confirmed germ cell tumor (GCT) based on pathologic review at INT Milan * Metastatic disease * Relapsed or refractory disease * Prior chemotherapy treatment for GCT without a pathologic diagnosis due to unequivocal clinical evidence of GCT and an urgent need to start therapy (elevated alpha-fetoprotein \[AFP\] or human chorionic gonadotropin \[HCG\] with pattern of metastases consistent with GCT and high tumor burden) allowed * Unequivocal progression of measurable disease, consisting of abnormalities on 2-dimensional imaging or raised tumor markers, following 1 line of cisplatin-based chemotherapy as documented by either of the following: * Tumor biopsy of new, growing, or unresectable lesions demonstrating viable non-teratomatous GCT (enrollment on this study for adjuvant treatment after resection of viable GCT not allowed) * Increasing or abnormally elevated serum tumor markers (HCG or AFP) (increasing lactate dehydrogenase \[LDH\] alone does not constitute progressive disease) * Received ≥ 3 and ≤ 6, cisplatin-based chemotherapy courses as part of first-line (initial) chemotherapy and ≤ 6 cisplatin-based chemotherapy courses * Brain metastases allowed * May be treated with radiotherapy and/or surgery concurrently with cisplatin, ifosfamide, and etoposide regimen * Radiotherapy should not be given concurrently with mobilization phase/leukapheresis and high-dose carboplatin and etoposide PATIENT CHARACTERISTICS: * WBC ≥ 2,000/µL * ANC ≥ 1,500/µL * Platelet count ≥ 100,000/µL * Creatinine clearance ≥ 50 cc/min (unless renal dysfunction is due to tumor obstructing the ureters, in which case eligibility will be determined by the principal investigator) * AST/ALT \< 2 times upper limit of normal (ULN) (\< 5 times ULN if due to hepatic metastases) * Total bilirubin \< 1.5 times ULN * Ejection fraction ≥ 50% by echocardiogram * Negative serology for the following infectious diseases: * HIV type 1 and 2 * Hepatitis B surface antigen (active carriers) * Hepatitis C * Cytomegalovirus (serum Ag p65 ± PCR confirmation at principal investigator discretion) PRIOR CONCURRENT THERAPY: * See Disease Characteristics * Recovered from prior surgery * At least 3 weeks since prior chemotherapy * No prior high-dose chemotherapy with peripheral blood stem cell rescue * No more than 1 prior chemotherapy regimen for metastatic disease