Combination Chemotherapy, Radiation Therapy, and an Autologous Peripheral Blood Stem Cell Transplant in Treating Young Patients With Atypical Teratoid/Rhabdoid Tumor of the Central Nervous System

Inclusion Criteria:

* Diagnosis of CNS atypical teratoid/rhabdoid tumor (AT/RT) or tumors that have a mutation of the INI1 gene (even if the tumor does not have the usual histologic characteristics of AT/RT)

  * Patients with extra neural metastasis (M4) or renal rhabdoid tumors are not eligible
  * Patients with MRI evidence of spinal disease are eligible
* Must have undergone definitive surgery in the past 31 days
* 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 or 10-28 days after surgery
* Entire spinal MRI must be obtained either pre-operatively (with gadolinium) or post-operatively (10-28 days after surgery), prior to study enrollment (with and without gadolinium)
* Life expectancy \> 8 weeks
* ANC \> 1,000/uL
* Platelet count \> 100,000/uL (transfusion independent)
* Hemoglobin \> 8 g/dL (RBC transfusions allowed)
* Creatinine clearance (minimum of 12-24 hour urine collection) or radioisotope GFR \>= 60 mL/min
* Total bilirubin =\< 1.5 times upper limit of normal (ULN) for age
* AST and ALT \< 2 times ULN for age
* Shortening fraction of \>= 27% by echocardiogram OR ejection fraction of \>= 47% by radionuclide angiogram
* No evidence of dyspnea at rest
* Pulse oximetry \> 94% on room air
* Not pregnant or nursing
* Negative pregnancy test
* Fertile patients must use effective contraception
* No prior radiotherapy or chemotherapy except for the following:

  * Patients enrolled on protocol ACNS0334 whose tumors demonstrate the INI1 gene mutation are eligible to transfer to this study even if they have received one course of induction therapy (these patients must be re-consented to treatment and restaged)
  * Prior corticosteroids allowed