Study of High-Dose Chemotherapy With Bone Marrow or Stem Cell Transplant for Rare Poor-Prognosis Cancers

Inclusion Criteria: * Patients must be ineligible for other IRB-approved myeloablative regimens, be 21 years old or younger, and must have a histologically-confirmed Wilms' tumor, liver cancer, recurrent brain tumor of childhood, nasopharyngeal carcinoma, fibrosarcoma, desmoplastic small round cell tumor, germ cell tumor or other small round cell tumor, which: 1. is metastatic and has \< 25% cure rate with conventional treatment; or 2. progressed after prior chemotherapy and has \< 25% salvage rate with non-myeloablative therapies. * Disease status: Within 3 weeks of initiation of this protocol, patients must: 1. be in a complete or good partial remission (section 7.4); or 2. have a "chemosensitive" tumor, which is defined as a \> 50% decrease in at least one measurable tumor parameter attributable to prior chemotherapy, without evidence of progressive disease by any other parameter. * Prior chemotherapy: Before entry to this protocol, patients must have derived maximal benefit from conventional, i.e., nonmyeloablative, doses of combination chemotherapy. Conventional therapy should be continued until either a complete remission is achieved, no further benefit from non-myeloablative dosing can be appreciated, or toxicity from conventional therapy is perceived as limiting in the absence of stem cell rescue. The cancer must be proven to be sensitive to alkylating agents. This means that, in addition to, or as part of, the appropriate chemotherapy protocol for the specific cancer in question, all patients must have received and responded to a minimum of: 1. 2 courses of high-dose cyclophosphamide, totaling \> 4200 mg/m2; or 2. courses of high-dose ifosfamide totaling \> 12 gm/m2. 3. 1 course of "a)" above, plus 1 course of 'b)" above. 4. Equivalent high dose alkylating agents as described in 3.3 a, b, and c. * Patients must have adequate renal hepatic, and cardiac function (sections 4.4-4.6). * Patients must meet at least one of the following stem cell requirements (Peripheral blood collection is to be preferred when available as an option): 1. Harvested bone marrow must contain 1 x 108 nucleated cells per kg of body weight, or, 2. Peripheral blood collection should include at least 2 x 106 CD34+ cells/kg. * Informed consent must be signed indicating patient and/or parental awareness of the investigational nature of this program