Inclusion Criteria:

* Newly diagnosed non-rhabdomyosarcoma soft tissue sarcoma (STS), confirmed by central pathology review via concurrent enrollment on protocol COG-D9902

* Metastatic or non metastatic disease
* Meets 1 of the following criteria:

* Intermediate (i.e., rarely metastasizing) or malignant STS, including any of the following:

* Adipocytic tumor, including liposarcoma of any of the following histology subtypes:

* Dedifferentiated
* Myxoid
* Round cell
* Pleomorphic type
* Mixed-type
* Not otherwise specified (NOS)
* Fibroblastic/myofibroblastic tumors, including any of the following:

* Solitary fibrous tumor
* Hemangiopericytoma
* Low-grade myofibroblastic sarcoma
* Myxoinflammatory fibroblastic sarcoma
* Adult fibrosarcoma\*
* Myxofibrosarcoma
* Low-grade fibromyxoid sarcoma or hyalinizing spindle-cell tumor
* Sclerosing epithelioid fibrosarcoma
* So-called fibrohistiocytic tumors, including any of the following:

* Plexiform fibrohistiocytic tumor
* Giant cell tumor of soft tissues
* Pleomorphic malignant fibrous histiocytoma (MFH)/undifferentiated pleomorphic sarcoma
* Giant cell MFH/undifferentiated pleomorphic sarcoma with giant cells
* Inflammatory MFH/undifferentiated pleomorphic sarcoma with prominent inflammation
* Smooth muscle tumor (leiomyosarcoma)
* Pericytic \[perivascular\] tumor (malignant glomus tumor or glomangiosarcoma)
* Vascular tumor, including angiosarcoma
* Chondro-osseous tumors of any of the following types:

* Mesenchymal chondrosarcoma
* Extraskeletal osteosarcoma
* Tumors of uncertain differentiation, including any of the following:

* Angiomatoid fibrous histiocytoma
* Ossifying fibromyxoid tumor
* Myoepithelioma/parachordoma
* Synovial sarcoma
* Epithelioid sarcoma
* Alveolar soft-part sarcoma
* Clear cell sarcoma of soft tissue
* Extraskeletal myxoid chondrosarcoma ("chordoid type")
* Malignant mesenchymoma
* Neoplasms with perivascular epithelioid cell differentiation (PEComa)
* Clear cell myomelanocytic tumor
* Intimal sarcoma
* Malignant peripheral nerve sheath tumor
* Dermatofibrosarcoma protuberans meeting both of the following criteria:

* Non metastatic disease
* Tumor must be grossly resected prior to study enrollment
* Embryonal sarcoma of the liver
* Unclassified STS that is too undifferentiated to be placed in a specific pathologic category (undifferentiated STS or STS NOS)
* Gross resection of the primary tumor ≤ 42 days prior to enrollment required except if any of the following circumstances apply:

* Non metastatic high-grade tumor > 5 cm in maximal diameter and gross or microscopic residual tumor is anticipated after resection
* Tumor of either high- or- low-grade that cannot be grossly excised without unacceptable morbidity
* High-grade tumor with metastases

* Patients with metastatic low-grade tumor whose disease is amenable to gross resection at all sites must undergo gross resection of all sites prior to study entry
* Patients with a tumor recurrence after a gross total resection are not eligible
* Tumors arising in bone are not eligible
* Patients with epithelioid sarcoma, clear cell sarcoma, or clinical or radiologic evidence of regional lymph node enlargement must undergo sentinel lymph node biopsies or lymph node sampling to confirm the status of regional lymph nodes\* NOTE: \*Except in cases where the study radiologist reviews the imaging and indicates that a biopsy is not needed to confirm that the patient has lymph node involvement.

* If lymph node biopsies are positive for tumor (or the lymph nodes are classified as positive by the study radiologist), formal lymph node dissection must be done at the time of definitive surgery(prior to study entry for patients assigned to study regimen C)
* Patients with metastatic disease must undergo a biopsy to confirm the presence of metastatic tumor if all metastases are < 1 cm in maximal diameter (except in cases where the study radiologist reviews the imaging and indicated that a biopsy is not needed to confirm that the patient has metastatic disease)
* Lansky performance status (PS) 50-100% (for patients ≤ 16 years of age) OR Karnofsky PS 50-100% (for patients > 16 years of age)
* Life expectancy ≥ 3 months
* Absolute neutrophil count ≥ 1,000/mm³\*
* Platelet count ≥ 100,000/mm³\*
* Creatinine clearance or radioisotope glomerular filtration rate ≥ 70 mL/min (≥ 40 mL/min for infants < 1 year of age)\* or serum creatinine based on age and/or gender as follows:

* 0.4 mg/dL (1 month to < 6 months of age)
* 0.5 mg/dL (6 months to < 1 year of age)
* 0.6 mg/dL (1 year to < 2 years of age)
* 0.8 mg/dL (2 years to < 6 years of age)
* 1.0 mg/dL (6 years to < 10 years of age)
* 1.2 mg/dL (10 years to < 13 years of age)
* 1.5 mg/dL (male) or 1.4 mg/dL (female) (13 years to < 16 years of age)
* 1.7 mg/dL (male) or 1.4 mg/dL (female) (≥ 16 years of age)
* Patients with urinary tract obstruction by tumor must meet the renal function criteria listed above AND must have unimpeded urinary flow established via decompression of the obstructed portion of the urinary tract
* Bilirubin ≤ 1.5 times upper limit of normal (ULN)\*
* Shortening fraction ≥ 27% by echocardiogram\* OR ejection fraction ≥ 50% by radionuclide angiogram\*
* Not pregnant or nursing (patients undergoing radiotherapy and/or chemotherapy)

* No nursing for ≥ 1 month after completion of study treatment in study regimens C or D
* Fertile patients must use effective contraception during and for ≥ 1 month after completion of study treatment
* Negative pregnancy test
* No evidence of dyspnea at rest\*
* No exercise intolerance\*
* Resting pulse oximetry reading > 94% on room air (for patients with respiratory symptoms)\*
* Prior treatment for cancer allowed provided the patient meet the prior therapy requirements
* No prior anthracycline (e.g., doxorubicin or daunorubicin) or ifosfamide chemotherapy for patients enrolled on arm C or arm D
* No prior radiotherapy to tumor-involved sites