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…