MIBG With Dinutuximab +/- Vorinostat

Inclusion Criteria: 1. Patients must have evidence of MIBG uptake into tumor at ≥ 1 site (bone or soft tissue) within 28 days prior to study entry and subsequent to any intervening therapy. 2. Patients must have a diagnosis of neuroblastoma either by histologic verification of neuroblastoma and/or demonstration of tumor cells in the bone marrow with increased urinary catecholamines. 3. Patients must have a history of high-risk neuroblastoma according to COG risk classification at the time of study registration. Patients who were initially considered low or intermediate-risk, but then reclassified as high-risk are also eligible. 4. All patients must have at least one of the following 1. Recurrent/progressive disease: after the diagnosis of high risk neuroblastoma at any time prior to enrollment regardless of response to frontline therapy 2. No prior history of recurrent/progressive disease since the diagnosis of high risk neuroblastoma b1) Refractory disease- a best overall response of no response/stable disease since diagnosis of high risk neuroblastoma and at least 4 cycles of induction therapy. No prior history of recurrent/progressive disease since the diagnosis of high risk neuroblastoma. b2) Persistent disease- a best overall response of no partial response since diagnosis of high risk neuroblastoma and at least 4 cycles of induction therapy. No prior history of recurrent/progressive disease since the diagnosis of high risk neuroblastoma. 5. Patients must have at least ONE of the following (lesions may have received prior radiation therapy as long as they meet the other criteria listed below): a) For recurrent/progressive or refractory disease, at least one MIBG avid bone site. b) For persistent disease, if a patient has 3 or more MIBG avid lesions, then no biopsy is required. If a patients has only 1 or 2 MIBG avid bone lesion sites then biopsy confirmation of neuroblastoma or ganglioneuroblastoma in at least one MIBG avid site present at the time of enrollment is required to be obtained at any time point prior to enrollment. c) For MIBG non-avid tumors, patients must have at least one FDG avid site and a biopsy confirmation of neuroblastoma and/or ganglioneuroblastoma at any time prior to enrollment from at least one FDG-avid site. 6. Any amount of neuroblastoma tumor cells in the bone marrow done at the time of study enrollment based on routine morphology with or without immunocytochemistry in at least one sample from bilateral aspirates and biopsies. 7. At least one soft tissue lesion that meets criteria for a TARGET lesion as defined by: a) SIZE: Lesion can be accurately measured in at least one dimension with a longest diameter ≥ 10 mm, or for lymph nodes ≥ 15 mm on short axis. Lesions meeting size criteria will be considered measurable. b) In addition to size, a lesion needs to meet one of the following criteria except for patients with parenchymal CNS lesions which only need to meet size criteria: b1) MIBG avid. For patients with recurrent/progressive or refractory disease, no biopsy is required. For patients with persistent disease only: If a patient has only 1 or 2 MIBG avid lesions sites, then biopsy confirmation of neuroblastoma and/or ganglioneuroblastoma in at least one MIBG avid site present at time of enrollment is required to be obtained. If a patient has 3 or more MIBG avid lesions, then no biopsy is required. b2) MIBG non avid tumors: Patients must have at least one FDG avid site and biopsy confirmation of neuroblastoma and/or ganglioneuroblastoma in at least one FDG-PET avid site present at the time of enrollment. 8. At least one non-target soft tissue lesion that is not measurable, but had a biopsy positive for neuroblastoma and/or ganglioneuroblastoma or is MIBG avid at any time prior to enrollment. 9. Patients must have a life expectancy of at least 12 weeks and a Lansky (≤16 years) or Karnofsky (\>16 years) score of at least 50. 10. Prior Therapy 1. Patients must have fully recovered from the acute toxic effects of all prior chemotherapy, immunotherapy, or radiotherapy prior to study registration. 2\. Patients must not have received the therapies indicated below after disease evaluation or within the specified time period prior to registration on this study as follows: 1\. Myelosuppressive chemotherapy: must not have received within 2 weeks prior to registration. 2\. Biologic anti-neoplastics- agents not known to be associated with reduced platelet or ANC counts (including retinoids): must not have received within 7 days prior to registration. 3\. Monoclonal antibodies: must have received last dose at least 7 days or 3 half-lives whichever is longer, but no longer than 30 days (with recovery of any associated toxicities), prior to protocol therapy. 4\. Cellular Therapy (e.g. modified T cells, NK cells, dentritic cells etc.): must not have received within 3 weeks and resolution of all toxicities. 5\. Radiation: must not have received small port radiation within 7 days prior to registration. 6\. Hematopoietic Stem Cell Transplant: 7. IVIG 8. Therapeutic MIBG 9. Investigational medicines covered under another IND 10. Medications interfering with MIBG uptake 11. Medications that prolong QTc (Part B only) 12. Valproic acid (Part B only) 11) All patients must have adequate organ function defined as: \- Hematological Function: 1. Absolute Phagocyte count (APC= neutrophils and monocytes): ≥ 1000/µL 2. Absolute Neutrophil count: ≥750/µL 3. Absolute Lymphocyte count ≥ 500/µL 4. Platelet count: ≥ 50,000/µL, transfusion independent (no platelet transfusions within 1 week) 5. Hemoglobin ≥ 10 g/dL (may transfuse) 6. Patients with known bone marrow metastatic disease will be eligible for study as long as they meet hematologic function criteria above. * Renal Function: Age-adjusted serum creatinine ≤ to 1.5 x normal for age/gender OR creatinine clearance or GFR greater than or equal to 60 cc/min/1.73m2 * Liver Function: Total bilirubin ≤ 1.5 x normal for age, AND SGPT (ALT) 135 and SGOT (AST) ≤ 3 x upper limit of normal. Sinusoidal obstruction syndrome (SOS) if present, must be stable or improving clinically * Cardiac Function: Normal ejection fraction documented by either echocardiogram or radionuclide MUGA evaluation OR Normal fractional shortening documented by echocardiogram * Pulmonary Function: No dyspnea at rest, no oxygen requirement. 12\) Reproductive Status: All post-menarchal females must have a negative beta-HCG. Males and females of reproductive age and childbearing potential must use effective contraception for the duration of their participation. 13\) Patients with other ongoing serious medical issues must be approved by the study chair prior to registration. 14\) Autologous peripheral blood stem cells (PBSC)•The minimum dose for peripheral blood stem cells is 2.0 x 106viable CD34+ cells/kg. Patients who do not meet this minimum requirement for available PBSCs are not eligible. •Only un-purged stem cells are allowed unless a center has separate FDA approval for infusion of purged stem cells. •For patients whose body weight exceeds ideal body weight (IBW) by more than 20%, adjusted body weight may be used for the calculation of PBSC dose 15) Physician deems that there is reasonable ability to obtain vorinostat via commercial supply (Part B Only) Exclusion Criteria: * Pregnancy, breast feeding, or unwillingness to use effective contraception during the study. * Patients who, in the opinion of the investigator, may not be able to comply with the safety monitoring requirements of the study. * Patients with disease of any major organ system that would compromise their ability to withstand therapy. * Patients who have received prior allogeneic stem cell transplant * Patients who have received prior solid organ transplantation * Patients must not have received prior total body irradiation * Prior HDAC inhibitor given in combination with therapeutic 131I-MIBG(Part B only) * The maximum total allowable dose of 131I-MIBG that can be given per institutional guidelines must be at least 90% of the calculated 131I-MIBG dose or the patient is not eligible. * Patients who are on hemodialysis. * Patients with an active or uncontrolled infection. * Known history of human immunodeficiency virus (HIV) infection, hepatitis B, or hepatitis C. * Patient declines participation in NANT 2004-05, the NANT Biology Study * Patients and/or families who are physically and psychologically unable to cooperate with the radiation safety isolation. * Patients with a history of having to discontinue anti-GD2 antibody therapy due to toxicity are not eligible. * Prior anti-GD2 therapy is not otherwise an exclusionary criteria unless it was given in combination with therapeutic 131I-MIBG.