Myeloablative Consolidation Therapy and Tandem Autologous Stem Cell Rescue in Patients With High-Risk Neuroblastoma

* Less than 30 years of age at diagnosis of neuroblastoma * End of Induction disease evaluation demonstrating CR, PR, MR or SD * Hematopoietic Recovery from last induction course of chemotherapy * No uncontrolled infection * Minimum frozen PBSCs of 2 x 10\^6 CD34 cells/kg for each transplant are mandatory and a PBSC of 2 x 10\^6 CD34 cells/kg for back-up are strongly recommended (thus, PBSC of no less than 6 x 10\^6 CD34 cells/kg is encouraged). These must all be collected prior to the initiation of consolidation. * Adequate organ function defined as: * Hepatic: AST and ALT \< 3 x upper limit of institutional normal; ALT ≤ 3 x ULN for age; total bilirubin ≤ 1.5 x ULN for age, if baseline was normal, \> 1.0 1.5 x baseline if baseline was abnormal * Cardiac: shortening fraction ≥ 27% or ejection fraction ≥ 45%, no clinical congestive heart failure * Pulmonary: no evidence of dyspnea at rest and norequirement for supplemental oxygen * Renal: Creatinine clearance or GFR \> 60 mL/min/1.73m\^2. If a creatinine clearance is performed at end induction and the result is \< 100 ml/min/1.73m\^2, a GFR must then be performed using a nuclear blood sampling method or iothalamate clearance method. Camera method is NOT allowed as measure of GFR prior to or during Consolidation therapy for patients with GFR or creatinine clearance of \< 100 ml/min/1.73m\^2 * Recovery from acute toxicities of last cycle of induction chemotherapy * Appropriate written consent - adult or parent/guardian if patient is \< 18 years of age and minor information sheet if patient is \> 8 years of age