Pyrazoloacridine and Stem Cell or Bone Marrow Transplantation in Treating Young Patients With High-Risk Neuroblastoma

Inclusion Criteria: * Patients must have a diagnosis of neuroblastoma (ICD-O morphology 9500/3) verified by histology and/or demonstration of clumps of tumor cells in bone marrow with elevated urinary catecholamine metabolites * Patients must meet one of the two following disease status criteria to enter on study; * Current or prior progressive disease (PD) by INRC criteria * Either mixed response (MR) or no response (NR) by INRC criteria following completion of minimum of 4 courses of induction therapy * Patients meeting disease status criteria in either category A or B must also have at least one of the following sites of disease present to enter on study: * At least one tumor lesion on CT or MRI scan that is \>= 20mm in at least one dimension (spiral CT lesion must be \>= 10mm in at least one dimension) * MIBG scan with positive uptake at a minimum of one site * Bone marrow disease documented by standard histology of bilateral bone marrow aspirate and biopsy specimens * Patients \> 16 years of age: Karnofsky \>= 50%; Patients =\< 16 years of age: Lansky \>= 50%; patients who are unable to walk because of paralysis, but who are up in a wheelchair will be considered ambulatory for the purpose of assessing the performance score; life expectancy must be \>= 2 months for all patients * Patients must have fully recovered from the acute toxic effects of all prior chemotherapy, immunotherapy, or radiotherapy prior to entering this study * Chemotherapy and/or biologics: Must not have received treatment within 3 weeks of entry onto this study (4 weeks if prior nitrosureas * Radiation: At least 4 weeks since last dose of radiation therapy to at least one lesion being used as criteria for study eligibility; only 2 weeks must elapse since the last dose of radiation (small port) to a lesion not used for study eligibility; at least 6 months must have elapsed since the last dose of prior craniospinal XRT and radiation to \>= 50% of the pelvis or TBI * Stem Cell Transplant (SCT): \>= 9 months must have elapsed since autologous hematopoietic stem cell transplant (aHSCT) * Prior MIBG therapy: At least 12 weeks must have elapsed since treatment with therapeutic doses of MIBG * Study specific limitations on prior therapy: patients who have a history of allogeneic HSCT are not eligible * Growth factor(s): At least 7 days since the last dose of any myeloid growth factor was given * Any patient considered for this protocol must meet the following criteria for minimum number of autologous stem cells sufficient to rescue hematopoiesis; a combination of products may be used to meet this requirement * All stem cell products infused on this protocol must meet the following criteria for tumor analysis: No tumor cells detectable by immunocytology OR for patients who had a PBSC collection done previously and no immunocytological testing was done on the product at the time of collection: This product may be used for infusion on this study if the patient's bilateral bone marrow aspirate and biopsy specimens can be shown to be tumor free by standard histology within 4 weeks of PBSC collection * Glomerular filtration rate (GFR) using blood draw method or 12 hour urine collection for creatinine clearance \>= 100 ml/min/1.73 m\^2 * Serum creatinine =\< 1.5 x upper limit of normal for age * Normal ejection fraction (\>= 55%) documented by echocardiogram or radionuclide MUGA evaluation OR normal fractional shortening (\>= 27%) documented by echocardiogram * Total bilirubin \< 1.5 x upper limit of normal * AST/ALT =\< 3 x upper limit of normal * Platelets \>= 75,000/uL (transfusion independent) * Hemoglobin \>= 8 g/dl (transfusion allowed) * Because evaluation of hematopoietic toxicity is essential to this study, the same criteria will be applied to patients with tumor infiltration of the bone marrow * Normal lung function as manifested by no dyspnea at rest and no oxygen requirement Exclusion Criteria: * No patients who are pregnant or lactating will be allowed to enter on study; pregnancy tests must be obtained in females who are post-menarchal; males and females of reproductive potential may not participate unless they have agreed to use an effective method of contraception while receiving therapy * Patients with active infections requiring intravenous antivirals, antibiotics, or antifungals; patients on prolonged antifungal therapy are still eligible if they are culture negative and biopsy negative in suspected residual radiographic lesions and they meet other organ function criteria; patients who are known HIV seropositive with stable disease and lack of major health problems who are not on anti-retroviral therapy, may be eligible at the discretion of the Study Chair * Prior treatment with Pyrazoloacridine (PZA) * Prior history of allogeneic HSCT * Neurologic Exclusions: * Acute or chronic CNS disease * History of seizures * History of cerebral bleeding or stroke * CNS parenchymal metastases as documented by head CT with contrast or head MRI with gadolinium performed within 30 days of study entry. Patients with epidural metastases causing mass effect on the brain are also excluded (skull metastases are allowed provided they are not associated with intracranial disease compressing or displacing the brain