Stem Cell Transplant for High Risk Central Nervous System (CNS) Tumors

Inclusion Criteria: * Patient's age must be greater than (\>) 18 months and less than or equal to (≤) 25 years at the time of diagnosis or recurrence. * Neuroradiographic evidence of a recurrent posterior fossa medulloblastoma or recurrent CNS germ cell tumor. * The presence of a histologically confirmed high grade astrocytoma, GBM, rhabdoid tumor, supratentorial PNET, or pineoblastoma either at the time of diagnosis or recurrence. * Patients must be brought to state of minimum residual disease by surgical reduction and/or chemotherapy and/or radiation therapy or a combination of above prior to myeloablative chemotherapy and tandem stem cell rescue. * Documentation of chemotherapy sensitivity is required for enrollment. Chemotherapy-sensitive tumors are defined as those tumors which have had a reduction of 50% after 2-4 cycles of chemotherapy (CTX or platinum). For patients with no evidence of disease post resection, continued complete remission after 2-4 cycles of chemotherapy defines chemosensitivity. * Adequate physiologic function, defined as follows: * creatinine clearance \> 70 ml/minutes/1.73 m2. * SGPT \< 10 x normal and bilirubin \< 10 mg/dl. * Adequate complete blood count (CBC): hemoglobin \> 10 gm/dl, absolute neutrophil count (ANC) \> 1500/ul, and platelets \> 100,000/ul. * Informed consent. The patient and/or the patient's legally authorized guardian must acknowledge in writing that consent to become a study subject has been obtained, in accordance with in…