Inclusion Criteria:

* Patients must be eligible for, and enrolled on D9902 prior to enrollment on ARST08P1
* Patients with newly diagnosed, biopsy-proven metastatic rhabdomyosarcoma or ectomesenchymoma (stage IV, clinical group IV) are eligible for this study; patients with stage IV, clinical group IV RMS with parameningeal and paraspinal primary tumors, including those with intracranial extension (ICE) are eligible for ARST08P1; ICE is defined by contrast magnetic resonance imaging (MRI) showing that the primary tumor touches, displaces, invades, distorts, or otherwise causes signal abnormality of the dura in brain or spinal cord in contiguity to the primary site; ICE is also presumed to exist if the cerebrospinal fluid (CSF) cytopathology is positive for tumor at diagnosis
* Patients must have a performance status corresponding to Eastern Cooperative Oncology Group (ECOG) scores of 0, 1, or 2; use Karnofsky for patients > 16 years of age and Lansky for patients =< 16 years of age
* No prior chemotherapy or radiotherapy except for use of corticosteroids or emergent radiation therapy; patients requiring emergency radiation are eligible
* Creatinine clearance or radioisotope glomerular filtration rate (GFR) >= 70 mL/min/1.73m\^2 OR maximum serum creatinine based on age/gender as follows:

* 0.4 mg/dL (for patients 1 to 5 months of age)
* 0.5 mg/dL (for patients 6 to 11 months of age)
* 0.6 mg/dL (for patients 1 year of age)
* 0.8 mg/dL (for patients 2 to 5 years of age)
* 1.0 mg/dL (for patients 6 to 9 years of age)
* 1.2 mg/dL (for patients 10 to 12 years of age)
* 1.5 mg/dL (males) or 1.4 mg/dL (females) (for patients 13 to 15 years of age)
* 1.7 mg/dL (males) or 1.4 mg/dL (females) (for patients >= 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
* Total bilirubin =< 1.5 x upper limit of normal (ULN) for age, unless there is evidence of biliary obstruction by the tumor
* Shortening fraction >= 27% by echocardiogram (ECHO) OR ejection fraction >= 50% by radionuclide angiogram
* Absolute neutrophil count (ANC) >= 750/uL; abnormal blood counts are permissible if there is bone marrow biopsy or aspirate proven bone marrow involvement by rhabdomyosarcoma
* Platelet count >= 75,000/uL; abnormal blood counts are permissible if there is bone marrow biopsy or aspirate proven bone marrow involvement by rhabdomyosarcoma
* Sexually active patients of childbearing potential must agree to use effective contraception during therapy (Pilots 1 and 2) and for at least 3 months after the last dose of IMC-A12 (Pilots 1)

Exclusion Criteria:

* Female patients who are pregnant are not eligible
* Female patients who are breastfeeding are not eligible; female patients who are lactating must agree to stop breastfeeding to participate in this study
* Patients receiving growth hormone therapy are not eligible
* Patients with known type I or type II diabetes mellitus are not eligible for enrollment on Pilot 1
* Patients with evidence of uncontrolled infection are not eligible
* All patients and/or their parents or legal guardians must sign a written informed consent
* All institutional, Food and Drug Administration (FDA), and National Cancer Institute (NCI) requirements for human studies must be met