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 institutional policies provided by the United States (U.S.) Department of Health and Human Services. * Protocol approval. Approval for the use of this institution's Human Rights Committee must be obtained in accordance with the institutional assurance policies of the U. S. Department of Health and Human Services. * Patients with high-risk medulloblastoma after initial surgery. * To allow non-English speaking patients to participate in this study, bilingual health care services will be provided in the appropriate language. Exclusion Criteria: * Patients with brain stem glioma are ineligible.