The prognosis for patients with metastatic Ewing's sarcoma family of tumors (ESF), rhabdomyosarcoma (RMS), and neuroblastoma (NBL) remains dismal, with less than 25% long-term disease-free survival. Though less grave, the prognosis for cure for other high-risk patients is approximately 50%. New treatment strategies, including the identification of highly active new agents, maximizing the dose intensity of the most active standard drugs, and the development of improved methods of consolidation to eradicate microscopic residual disease, are clearly needed to improve the outcome of these patients. This protocol will address these issues by commencing with a Phase II window, for the highest risk patients, to evaluate a series of promising drugs with novel mechanisms of action. All patients will then receive 5 cycles of dose-intensive "best standard therapy" with doxorubicin (adriamycin), vincristine, and cyclophosphamide (VAdriaC). Patients at high risk of relapse will continue onto a phase I consolidation regimen consisting of three cycles of dose-escalated Melphalan, Ifosfamide, Mesna, and Etoposide (MIME). Peripheral blood stem cell transfusions (PBSCT) and recombinant human G-CSF will be used as supportive care measures to allow maximal dose-escalation of this combination regimen.