Combination Chemotherapy Followed By Peripheral Stem Cell Transplant in Treating Young Patients With Newly Diagnosed Supratentorial Primitive Neuroectodermal Tumors or High-Risk Medulloblastoma

Inclusion Criteria:

* High-risk medulloblastoma defined by any of the following:

  * \> 1.5 cm\^2 residual disease for any medulloblastoma histology, or
  * Lumbar cerebral spinal fluid (CSF) cytology positive for tumor cells by analysis of fluid collected either before definitive surgery or at least 10 days after definitive surgery unless contraindicated, or
  * Magnetic resonance imaging (MRI) evidence of M2 or M3 metastatic disease, or
  * M4 disease
* Supratentorial primitive neuroectodermal tumor (PNET) (any M-stage) will be eligible for study entry
* Children less than 8 months of age at the time of definitive surgery with or without measurable radiographic residual tumor with M0 stage medulloblastoma will be eligible for study entry
* Patients with anaplastic medulloblastoma are eligible regardless of M-stage or residual tumor
* Patients with M0 classic, non-desmoplastic medulloblastoma (R1) with radiographically measurable residual disease \< 1.5 cm\^2 are eligible
* Cranial MRI (with and without gadolinium) must be done pre-operatively; post-operatively, cranial MRI (with and without gadolinium) must be done, preferably within 48 hours of surgery; entire spinal MRI must be obtained either pre-operatively (with gadolinium) or post-operatively (at least 10 days following surgery) prior to study enrollment (with and without gadolinium); patients with MRI evidence of spinal disease are eligible for this study
* Evaluation of lumbar CSF cytology (cytospin preparation for microscopic evaluation) must be performed either pre-operatively or at least 10 days after definitive surgery unless contraindicated
* Patient must have a life expectancy \> 8 weeks
* Patient must have received no prior radiation therapy or chemotherapy other than corticosteroids; corticosteroids are allowable for all patients
* Creatinine clearance or radioisotope glomerular filtration rate \>= 60 mL/min
* Total bilirubin =\< 1.5 x upper limit of normal (ULN) for age, and
* Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) and serum glutamic pyruvic transaminase (SGPT) (alanine transaminase \[ALT\]) \< 2 x ULN for age
* Shortening fraction \>= 27% by echocardiogram, or
* Ejection fraction \>= 47% by radionuclide angiogram
* No evidence of dyspnea at rest
* Pulse oximetry \> 94% on room air
* Peripheral absolute neutrophil count (ANC) \> 1,000/uL
* Platelet count \> 100,000/uL (transfusion independent)
* Hemoglobin greater than 8 g/dL (may have received red blood cell \[RBC\] transfusions allowed)
* Hold trimethoprim/sulfamethoxazole (Bactrim) on the day of high-dose methotrexate (HDMTX) infusion and continue to hold until the methotrexate level is less than 0.1 micromolar (1 x 10-7 M)
* Avoid probenecid, penicillins, cephalosporins, aspirin, proton pump inhibitors and nonsteroidal anti-inflammatory drug (NSAIDS) on the day of methotrexate and continue until the methotrexate level is less than 0.1 micromolar (1 x 10-7 M) as renal excretion of methotrexate is inhibited by these agents
* Avoid IV contrast media, urinary acidifiers, phenytoin, and fosphenytoin on the day of methotrexate and until the methotrexate level is less than 0.1 micromolar (1 x 10-7 M)
* Concurrent use of enzyme inducing anticonvulsants (e.g. phenytoin, phenobarbital, and carbamazepine) should be avoided
* Clinically significant drug interactions have been reported when using vincristine with strong cytochrome P450 (CYP450) family 3 subfamily A member 4 (3A4) inhibitors and inducers; selected strong inhibitors of cytochrome P450 3A4 include azole antifungals, such as fluconazole, voriconazole, itraconazole, ketoconazole, and strong inducers include drugs such as rifampin, phenytoin, phenobarbitol, carbamazepine, and St. John's wort; the use of these drugs should be avoided with vincristine
* All patients and/or their parents or legal guardians must sign a written informed consent
* All institutional, Food and Drug administration (FDA), and National Cancer Institute (NCI) requirements for human studies must be met