DISEASE CHARACTERISTICS: Histologically confirmed sarcomas in the following categories: Soft tissue sarcoma (STS) High-grade STS of the extremities Primary extending to fascia or locally recurrent At least 10 cm in greatest dimension or multifocal on surgical pathology Primary site controlled by surgery and/or radiotherapy High-grade truncal or head and neck sarcoma At least 10 cm in greatest dimension or any size with no surgical options for clear margins Primary site controlled by surgery and/or radiotherapy Locally recurrent disease in CR or PR after surgery, chemotherapy, or radiotherapy Metastatic STS in CR or PR after surgery, chemotherapy, or radiotherapy Osteosarcoma (OS) Extremity OS after neoadjuvant chemotherapy and surgical resection provided: Less than 50% necrosis in the surgical specimen LDH or alkaline phosphatase greater than 2 times normal at presentation Axial OS in CR or PR after chemotherapy and/or surgery Primary or recurrent metastatic OS in CR or PR after chemotherapy, surgery, and/or radiotherapy Ewing's sarcoma or primitive neuroectodermal tumor Primary site in CR or PR after chemotherapy, radiotherapy, or surgery Rib, pelvic, or axial skeleton primary Bulky tumor (at least 10 cm in greatest diameter) Primary or recurrent metastatic disease in CR or PR after surgery, chemotherapy, or radiotherapy Rhabdomyosarcoma Gross residual disease after primary treatment with surgery, chemotherapy, and radiotherapy Primary group IV or recurrent metastatic disease in CR or PR after chemotherapy and radiotherapy with or without surgery No brain metastasis No histologically confirmed bone marrow metastasis Prior metastases allowed with clearing of bone marrow at entry No contraindication to collection of mobilized stem cells or, if needed, autologous bone marrow

PATIENT CHARACTERISTICS: Age: 10 to 55 Performance status: Karnofsky 80-100% Hematopoietic: Absolute neutrophil count greater than 2,000/mm3 Platelet count greater than 150,000/mm3 Hemoglobin greater than 10 g/dL Hepatic: See Disease Characteristics Bilirubin less than 1.5 mg/dL AST and ALT less than 3 times normal Hepatitis B surface antigen negative Negative hepatitis C antigen test required in patients with hepatitis C antibody Renal: Creatinine less than 1.4 mg/dL Creatinine clearance greater than 75 mL/min Cardiovascular: LVEF at least 55% by MUGA or echocardiogram No history of significant cardiac disease Pulmonary: FEV1 greater than 2 liters PaO2 greater than 70 mm Hg on room air PaCO2 less than 42 mm Hg on room air DLCO greater than 60% predicted Other: No hearing loss of greater than 40 decibels HIV negative No organic or psychiatric CNS dysfunction that would preclude study No other medical or psychosocial problems that would place patient at unacceptable risk No history of other malignancy except nonmelanoma skin cancer or carcinoma in situ of the cervix Not pregnant Negative pregnancy test Fertile patients must use effective contraception

PRIOR CONCURRENT THERAPY: More than 2 weeks since treatment to control primary or recurrent tumor Biologic therapy: Not specified Chemotherapy: See Disease Characteristics No more than 2 prior chemotherapy regimens (including adjuvant therapy) Prior cumulative cisplatin dose less than 400 mg/m2 Prior cumulative doxorubicin dose less than 240 mg/m2 Endocrine therapy: Not specified Radiotherapy: See Disease Characteristics No prior radiotherapy to more than 20% of the bone marrow-containing axial skeleton No prior radiotherapy to the left chest wall Surgery: See Disease Characteristics