Sirolimus in Combination With Metronomic Chemotherapy in Children With High-Risk Solid Tumors

Inclusion Criteria: * Subjects must be ≥ 12 months and ≤ 30 years of age at the time of study enrollment. * Subjects must have one of the following high-risk malignant pediatric extracranial solid tumors and be in complete remission or have minimal abnormalities on imaging studies after completion of upfront therapy administered with curative intent (cohort 1) or after completion of initial relapse regimen. * Prospective Cohort 1: * Metastatic/unresectable osteosarcoma, metastatic Ewing or Ewing-like sarcoma, high-risk rhabdomyosarcoma, metastatic non-rhabdomyosarcoma soft tissue sarcoma, desmoplastic small round cell tumor (DSRCT), malignant rhabdoid tumor. * Additional high-risk solid tumors at the request of the treating physician after approval by the study chair. * Primary central nervous system (CNS) tumors and lymphomas are not eligible. * Prospective Cohort 2: Recurrent extracranial solid tumor (any histology) in second complete remission following completion of initial relapse regimen. * Subjects must have had histologic verification of malignancy at original diagnosis or relapse. * Subjects must be in complete remission or with minimal radiological abnormalities. Baseline imaging should be the end of therapy imaging obtained at the completion of "standard" upfront therapy (cohort 1) or at the completion of initial relapse regimen (cohort 2). * Karnofsky ≥ 50% for subjects \> 16 years of age and Lansky ≥ 50% for subjects ≤ 16 years of age. * Subjects must have fully recovered from the acute non-hematologic toxic effects of all prior anti-cancer therapy and meet hematologic count parameters. Chronic non-hematologic toxic effects of prior anti-cancer therapy (ie peripheral neuropathy) must be improved to at least grade 2 and be stable or improving on current management. * Adequate bone marrow function defined as absolute neutrophil count (ANC) ≥ 750/μL and platelet count ≥ 50,000/μL (transfusion independent, defined as not receiving platelet transfusions within 7 days prior to enrollment). * Adequate renal function defined as creatinine clearance or radioisotope glomerular filtration rate (GFR) 70ml/min/1.73 m2 or serum creatinine based on age/gender values derived from the Schwartz formula for estimating GFR utilizing child length and stature data published by the Centers for Disease Control and Prevention (CDC). * Adequate liver function defined as: total bilirubin ≤ 2x upper limit of normal (ULN), and aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 225 U/L (5x the ULN). * Serum triglyceride level ≤300 mg/dL and serum cholesterol ≤ 300 mg/dL. * Random blood glucose ≤ 1.5x ULN for age. * Adequate pulmonary function defined as normal pulmonary function tests (PFTs), if there is a clinical indication for determination (dyspnea at rest, known requirement for supplemental oxygen). For subjects who do not have respiratory symptoms (no dyspnea at rest, O2 sat ≥ 93% on room air), PFTs are not required. Exclusion Criteria: * Pregnant or breast-feeding women will not be entered on this study as there may be fetal risks or teratogenic toxicities. Pregnancy tests must be obtained in girls who are post-menarchal. Males or females of reproductive potential may not participate unless they have agreed to use an effective contraceptive method during treatment and for 3 months after stopping treatment. * Concomitant Medication * Subjects receiving corticosteroids must be on a stable or decreasing dose of corticosteroid for the prior 7 days. * Subjects who are currently receiving enzyme inducing anticonvulsants are not eligible. * Subjects must not be receiving potent CYP3A4 inducers or inhibitors. * Subjects who are currently receiving another investigational drug are not eligible. * Subjects who are currently receiving any other anti-cancer agents are not eligible. * Subjects who have an uncontrolled infection are not eligible. * Subjects enrolled on a clinical trial for upfront therapy or relapse therapy for those patients in second complete remission. * Subjects who in the opinion of the investigator may not be able to comply with the safety monitoring requirements of the study are not eligible.