Ribociclib in Combination With Everolimus and Dexamethasone in Relapsed ALL

This research study is evaluating a drug called ribociclib (LEE011) given in combination with everolimus and other standard of care chemotherapy drugs as a possible treatment for relapsed or refractory ALL. The names of the drugs involved in this study are: * ribociclib * everolimus * dexamethasone

This research study is a Phase I clinical trial, which tests the safety of an investigational drug or a combination of drugs. Phase I studies try to define the appropriate dose of the investigational drug to use for further studies. "Investigational" means that the drug and the combination of drugs are still being studied. The FDA (the U.S. Food and Drug Administration) has not approved the study drugs, ribociclib or everolimus, for relapsed ALL, but these drugs have been approved for other uses. Ribociclib is a chemotherapy drug that is approved by the FDA for the treatment of certain types of breast cancer. It has also been studied in children and adults with other types of cancer. Information from these research studies has suggested that ribociclib may also be effective in treating participants with leukemia that did not respond to standard treatment or participants with leukemia that has come back after standard treatment. The growth and survival of leukemia cells is controlled by proteins within the cancer cell. The study drug, ribociclib, blocks a specific type of protein called a cyclin-dependent kinases (CDK). Laboratory and other studies suggest that when ribociclib blocks CDKs, cancer cells stop growing. Everolimus is a chemotherapy drug that is approved by the FDA for the treatment of breast cancer, neuroendocrine tumor and kidney cancer. Laboratory and other studies suggest that everolimus may prevent leukemia cell growth and also that it has been shown to increase the effectiveness of other chemotherapy drugs, including ribociclib. It has been studied in hundreds of people with various types of cancer as a single agent (a drug that is used alone to treat the cancer) or in combination with a number of other drugs. The drug combination of ribociclib and everolimus has not been previously tested in children, though these agents have been used together in adults with breast cancer. In this research study the investigators are looking to learn more about how ribociclib and everolimus work in combination with other standard of care drugs commonly used to treat relapsed/refractory leukemia. The main goals of the study are: * To evaluate the side effects (good and/or bad) of giving ribociclib in combination with other standard of care drugs. * To determine the highest dose of ribociclib and everolimus that can be given safely in combination with other standard of care drugs. * To determine the amount of ribociclib and everolimus in the blood when it is given in combination with other standard of care drugs.