A stem cell product collected prior to the infusion of Sm-EDTMP must be available, either by peripheral stem cell mobilization or bone marrow harvest prior to trial entry; a minimum of x ^ cluster of differentiation (CD)+ cells/kg ideal body weight is required Subjects must be at least kg or pounds to be eligible for stem cell donation Subjects must be at least kg or pounds to be eligible for stem cell donation RETREATMENT WITH MODIFIED T-CELLS INCLUSION CRITERIA: Subject has < % detectable modified T cells in peripheral blood (can be done at any time prior) RETREATMENT WITH MODIFIED T-CELLS INCLUSION CRITERIA: Subject has evidence of persistence of leukemic cells OR has CD+ B cell recovery detected within year of initial T cell infusion Patient must have an adequate supply of stem cells for transplant harvested prior to study enrollment, with adequate supply defined as x ^ cluster of differentiation (CD)+ cells/kg for peripheral blood stem cells (PBSC); cell mobilization method will be left up to the treating physician's discretion and may include mobilization growth factor alone or mobilization after chemotherapy; if patient is unable to mobilize the proper amount of peripheral stem cells, bone marrow may be harvested as the source of hematopoietic stem cells; in this instance, x ^ mononuclear cells/kg will be considered adequate; if necessary, a combination of peripheral stem cells and bone marrow can be used Collection of an adequate number of CD+ stem cells, i.e. >= - x ^/kg from apheresis Have at least million x e CD+ cells/kg to be infused Inability to purify >= . x ^ CD-enriched cells/kg of patient weight from the pooled G-CSF mobilized leukapheresis products Has sufficient CD CAR T cell product (x^ CAR T cells/kg) meeting release criteria for infusion Has sufficient CD CAR T cell product (x^ CAR T cells/kg) meeting release criteria for re-infusion Minimum frozen PBSCs of x ^ cluster of differentiation (CD) cells/kg for each transplant are mandatory and a PBSC of x ^ CD cells/kg for back-up are strongly recommended (thus, PBSC of no less than x ^ CD cells/kg is encouraged); these must all be collected prior to the initiation of consolidation All patients eligible for therapeutic study must have (>= x ^ CD/kg) autologous hematopoietic stem cells harvested and cryopreserved Patients who receive greater than mCi/kg are required to have stem cell rescue products harvested prior to study treatment; a minimum frozen autologous peripheral blood stem cell (PBSC) collection of x ^ cluster of differentiation (CD)+ cells/kg as aliquots is the suggested dose; for subjects receiving < mCi/ kg, a backup of . X ^ viable CD+ cells/kg purged or unpurged PBSC is strongly recommended but not required Patients will be enrolled at collection of at least . x ^ CD cells/kg of autologous hematopoietic progenitor cells (HPC-A) by apheresis; a minimum of collection procedures is required, unless collection on day # > . x ^, CD cells/kg; a maximum of collections is allowed; bone marrow harvest to supplement apheresis is not allowed RETREATMENT WITH MODIFIED T CELLS: Subject has < % detectable modified T cells in peripheral blood (can be done any time prior) Prior failed (< x ^ CD/kg) peripheral blood stem cell (PBSC) collection Prior therapy with neural stem cells If a patient does not have a hematopoietic stem cell product available for re-infusion after MIBG treatment, they may not receive a I-MIBG dose > mCi/kg; patients must have a hematopoietic stem cell product available for reinfusion after MIBG treatment at doses of > mCi/kg; the minimum quantity for peripheral blood stem cells is . x ^ cluster of differentiation [CD]+ cells/kg (optimum > x ^ CD+ cells/kg); the minimum dose for bone marrow is . x ^ mononuclear cells/kg (optimum > . x ^ mononuclear cells/kg) Must have at least one additional aliquot of >= x ^ CD/kg cryopreserved cells stored at the time of transplant Availability of autologous peripheral blood stem cell graft, containing at least . x ^ cluster of differentiation positive (CD+) cells/kg Patients will be enrolled after receiving at least two cycles of salvage cytoreductive chemotherapy and collection of at least . x ^ CD cells/kg of autologous hematopoietic progenitor cells (HPC-A) by apheresis; a minimum of collection procedures is required, unless collection on day # > . x ^ CD cells/kg; a maximum of collections is allowed; bone marrow harvest to supplement apheresis is not allowed Stem cells: patients must have an autologous hematopoietic stem cell product cryopreserved and available for re-infusion after I-H treatment; the minimum dose for hematopoietic stem cells is x ^ cluster of differentiation (CD)+ cells/kg Patients with stored autologous stem cells will be allowed A minimum apheresis collection of million cluster of differentiation (CD)+ cells/kg of autologous hematopoietic progenitor cells (AHPC) Must have ? x ^ NCs/kg BW OR x ^/kg BW CD-positive cells available for transplantation Total Collection of >= x ^ CD cells/kg prior to transplant one 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 x ^ CD+ cells/kg INCLUSION CRITERIA FOR CCT: 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 x ^ CD+ cells/kg Patients with stored stem cells will be treated at the escalating dose while patients with no stem cells will be treated at the mCi dose; neuroblastoma patients can be treated at the mCi dose with or without stored stem cells Adequate cell dose > .x^ CD+ cells/kg The minimum dose for peripheral blood stem cells is: PURGED PBSC: . x ^ viable CD+ cells/kg; UNPURGED PBSC: . x ^ CD+ cells/kg (immunocytology is not required for peripheral blood stem cells) Availability of autologous peripheral blood stem cell graft, containing at least . x ^ CD+ cells/kg Prior apheresis of >= million CD+ cells/Kg. Adequate autologous stem cell collection, defined as an unmanipulated, cryopreserved, peripheral blood stem cell collection containing at least x ^ cluster of differentiation (CD)+ cells/kg based on patient body weight Subjects must complete the filgrastim (G-CSF)/plerixafor mobilization of peripheral blood progenitor cells and must have collected at least . x ^ CD+ cells/kg, sufficient for preparation of both, a back-up of . x ^ CD+ cells and the research product Subjects must have collected at least x ^ CD+ cells/kg by apheresis after cycle Has had a successful peripheral blood stem cell collection with G-CSF (filgrastim) +/- plerixafor (Mozobil) only; the target cell dose is >= . x^ CD+ cells/kg An adequate number of cryopreserved GD-CAR cells must be available, or an adequate number of cryopreserved PBMC from the original apheresis must be available to generate a second dose of GD-CAR T cells; post-GD CAR apheresis will not be used to harvest peripheral blood mononuclear cell (PBMC) cells for the transduction for the second infusion Patient has had prior therapy with neural stem cells All patients eligible for therapeutic study must have a minimum of >= x ^ CD/kg autologous hematopoietic stem cells harvested and cryopreserved Autologous graft with a minimum of >= . x ^ CD+ cells/kg; not CD selected All patients eligible for therapeutic study must have a minimum of >= x^ CD/kg autologous hematopoietic stem cells harvested and cryopreserved and divided into aliquots of at least >= x^ CD/kg each; patients with a history of prior autologous hematopoietic cell transplant (HCT) are only required to have >= x^ CD/kg stored Patients must have a dose of unpurged peripheral blood stem cells is . x viable CD+ cells/kg available. Available CD+ stem cells All patients eligible for therapeutic study must have a minimum of >= x^ CD/kg autologous hematopoietic stem cells harvested and cryopreserved Available autologous stem cells: >= x ^ CD+ cells/kg More than x ^ autologous CD+ cells/kg cryopreserved. The graft may not be CD+ selected or otherwise manipulated to remove tumor or other cells. The graft can be collected at the transplanting institution or by a referring center Patients must have an adequate number of cluster of differentiation (CD)+ stem cells collected to allow for transplantation (defined as >= x ^ CD+ cells/kg body weight); if not previously collected and stored or if previous collection was inadequate, the patients must be willing to undergo stem cell mobilization and collection as per standard practice Diagnosis of CML except patients who have evidence of residual or persistent disease (morphologic, cytogenetic, or molecular) after a prior donor leukocyte infusion with a minimum cell dose of x ^ cells/kg Subjects in whom the minimum stem cell dose of . x ^ CD+ cells/kg has been collected PRIOR TO HIGH-DOSE CHEMOTHERAPY: Minimum of x^ CD+ cells/kg collected at mobilization Able to collect >= . x ^ CD+/kg cell for transplantation Inability to collect adequate stem cells No contraindication to the collection of a minimum of x ^ CD+ cells/kg by apheresis Patients with adequate autologous stem cell collection for transplantation (target >= . x ^ CD+ cells/kg) Patient has had prior treatment with mesenchymal stem cells (MSCs), including remestemcel-L. Adequate autologous graft, defined as an unmanipulated, cryopreserved, peripheral blood stem cell graft containing at least x ^ cluster of differentiation (CD)+ cells/kg based on patient body weight Other patient eligibility requirements\r\n * Human immunodeficiency virus (HIV) and HIV negative\r\n * Not pregnant or at risk for pregnancy and willing to use acceptable birth control methods\r\n * No uncontrolled drug of alcohol abuse; patients will be screened for drug and alcohol abuse by a pediatric psychologist who is a member of the HSCT team; this information will not be recorded in the patients hospital chart\r\n * Signed informed consent by patient or legal guardian in accordance with research ethics board guidelines or institutional review board (IRB)\r\n * Lansky or Karnofsky performance score of , or \r\n * Suitable haploidentical donor available\r\n * Cryopreserved autologous stem cells (minimum x ^ cluster of differentiation [CD]+ cells/kg) available for infusion for patient with solid tumors; subjects with solid tumors who have not had stem cells collected for clinical purposes prior to enrolling in the study will undergo autologous stem cell harvest following standard clinical procedures before beginning the study conditioning regimen Availability of previously collected autologous stem cells (at least . x ^ cluster of differentiation [CD] cells/kg) Patient must have cluster of differentiation (CD)+ stem cells >= x ^/kg (actual body weight of the recipient) available for transplantation Subjects are to receive autologous PBSC transplant following mobilization, CD+ cells collected by apheresis, and conditioning chemotherapy Subjects must have CD+ collection which allows reinfusion of ?. x and ?. x CD+ cells/kg