Iodine I 131 Metaiodobenzylguanidine in Treating Patients With Recurrent, Progressive, or Refractory Neuroblastoma or Malignant Pheochromocytoma or Paraganglioma

Inclusion criteria for NB: * Patients must have the diagnosis of NB in accordance with the International Criteria, i.e., either histopathology (confirmed by the MSKCC Department of Pathology) or BM involvement plus elevated urinary catecholamines. * Must have a history of tumor progression or recurrence or failure to achieve complete response with standard therapy. * Patients must have MIBG-avid NB and evaluable disease on MIBG scan at time of enrollment on protocol * Prior Therapy: At least 2 weeks should have elapsed since any biologic therapy. Three weeks should have elapsed since last dose of chemotherapy. * Age \>1 year * Determination that radiation safety restrictions during therapy period can be implemented. * Stem cells: Patients for high does must have an autologous hematopoietic stem cell product cryopreserved and available for re-infusion after MIBG treatment. Patients for low dose do not require cryopreserved autologous hematopoietic stem cell product available. The minimum dose for peripheral blood stem cells is 2 X106 CD34+ cells/kg. * Minimum life expectancy of eight weeks * Signed informed consent indicating awareness of the investigational nature of this program. Inclusion criteria for malignant CCT: * Patients must have the diagnosis of malignant CCT i.e. malignant pheochromocytoma or malignant paraganglioma * Patients must have MIBG-avid malignant CCT and evaluable disease on MIBG scan at time of enrollment on protocol * Prior Therapy: At least 2 weeks should have elapsed since any biologic therapy. Three weeks should have elapsed since last dose of chemotherapy. * Age between 1 and 21 years and able to cooperate with radiation safety restrictions during therapy period * Stem cells: Patients must have an autologous hematopoietic stem cell product cryopreserved and available for re-infusion after MIBG treatment. The minimum dose for peripheral blood stem cells is 2 X106 CD34+ cells/kg. * Minimum life expectancy of eight weeks. * Signed informed consent indicating awareness of the investigational nature of this program. Exclusion Criteria: * Severe major organ toxicity. Specifically, renal, cardiac, hepatic, pulmonary, gastrointestinal and neurologic toxicity should all be grade 2 or less. A grade 3 hearing deficit is acceptable. * Active serious infections not controlled by antibiotics. * Pregnant women are excluded for fear of danger to the fetus. Therefore negative pregnancy test is required for all women of child-bearing age, and appropriate contraception is used during the study period. * Inability or unwillingness to comply with radiation safety procedures or protocol requirements.