 Two to six participants will receive the starting dose of everolimus. If the side effects are not too severe, the next group of participants will take the study drug at a higher dose level. Up to two dose levels of the study drug will be tested. The main purpose of the study is to find the maximum tolerated dose of everolimus when used together with standard chemotherapy. Everolimus has been found to be safe and effective in adults and children for treatment of T- and B-cell leukemias and lymphomas. 