The goal of this study is to find a safe dose of sirolimus that can be used with a standard dose of L-asparaginase. To find the safe dose, the investigators will give the first patient a very small dose of sirolimus (smaller than the dose used in organ transplant children) and the standard dose of L-asparaginase. The investigators will then look for side effects. If side effects develop, the investigators will decrease the dose of sirolimus. If they do not, the investigators will increase the dose of sirolimus in the next patient on the study. The investigators will continue this method until fewer than one-third of patients have a side effect that would require stopping the drug or changing the dose.