Whole-Body Radiation Therapy, Systemic Chemotherapy, and High-Dose Chemotherapy Followed By Stem Cell Rescue in Treating Patients With Poor-Risk Ewing Sarcoma

Inclusion Criteria: * Patients with relapsed Ewing's sarcoma or primitive neuroectodermal tumor (PNET) with bony/soft tissue metastasis who achieved at least partial response (PR) to chemotherapy, surgery or radiotherapy * Newly diagnosed patients with metastatic disease to the bones: patients with metastatic Ewing's or metastatic PNET who achieved at least partial response (PR) to chemotherapy, surgery or radiotherapy are eligible * Ewing's sarcoma/PNET histology confirmed by Anatomic Pathology Department; histological confirmation of relapse is highly recommended but not mandatory * Patients must have documented at least partial response (PR) to previous therapy regimens; previous modalities may include surgery, chemotherapy, or radiation therapy; radiation must not include lung fields; only patients in CR or PR at the primary site will be eligible * Patients must have metastatic/recurrent disease identified by WB-MRI at the time of study entry; intensity-modulated radiation therapy (IMRT) can be delivered per protocol guidelines to at least one but not more than five primary/metastatic sites * Patients must have Karnofsky performance status \> 60% OR Lansky performance status \> 50% for patients younger than 16 years old * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control or abstinence) prior to study entry and for six months following duration of study participation; should a woman become pregnant or suspect that she is pregnant while participating on the trial, she should inform her treating physician immediately * Adequate number of autologous stem cells collected and cryopreserved prior to starting the study treatment * Creatinine clearance (12 or 24 hour urine collection) or glomerular filtration rate (GFR) \> 60 ml/min/1.73 m\^2 * Ejection fraction \> 50% by echocardiogram or multiple gated acquisition (MUGA) * Bilirubin \< 2 x upper limit of normal * Serum glutamic oxalo-acetic transaminase (SGOT) and serum glutamate pyruvate transaminase (SGPT) \< 5 x upper limit of normal * Platelet count \> 50,000/ul * Absolute granulocyte count \>= 750/ul * Forced expiratory volume in one second (FEV1) \> 2 liters adults (older than 16 years) * Room air arterial oxygen pressure (PaO2) \> 70 mm Hg adults (older than 16 years) * Room air partial pressure of carbon dioxide (PaCO2) \< 42 mm Hg adults (older than 16 years) * Diffusion capacity of carbon monoxide (DLCO) \> 50% predicted * If unable to cooperate with pulmonary function testing due to young age, then pulse oximetry \>= 94% children (younger than 16 years) * Pretreatment tests must have been performed within 4 weeks prior to initiation of protocol treatment * No other medical and/or psychosocial problems which, in the opinion of the primary physician or principal investigator, would place the patient at unacceptable risk from this regimen * Greater than 2 week period of recovery from prior modality used to control primary or recurrent site * All subjects or their legal guardians must have the ability to understand and the willingness to sign a written informed consent Exclusion Criteria: * Patients should not have any uncontrolled illness including ongoing or active infection * Patients may not be receiving any other investigational agents, concurrent biological agents, or chemotherapy * Patients must not have received prior chemotherapy or radiation within 2 weeks before study enrollment, and those who have not recovered from the adverse events due to agents administered more than 2 weeks earlier are excluded * Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated on this study * Patients with other active malignancies are ineligible for this study * Patients with prior treatment with myeloablative therapy are excluded * Karnofsky performance status \< 60% or Lansky performance status \< 50% for patients younger than 16 years old * Patients who require irradiation to more than 5 disease sites are excluded * Subjects who, in the opinion of the investigator, may not be able to comply with the safety monitoring requirements of the study