Rasburicase in Patients at High Risk for Tumor Lysis Syndrome (TLS) During Cycle-2

Study Drugs: Rasburicase is designed to help decrease or prevent the high level of uric acid that may occur during the beginning of chemotherapy. A high level of uric acid results from TLS and can lead to kidney failure. Allopurinol is designed to help block uric acid. It is the standard of care for helping to control increased uric acid levels caused by TLS. Study Groups and Drug Administration: Each cycle will last about 3 weeks. If you are found to be eligible to take part in this study, you will receive rasburicase by vein over about 30 minutes on Day 1 of Cycle 1 (about 4 hours before you begin receiving chemotherapy). If the doctor thinks it is needed, you may also receive the drug on Days 2-5 of Cycle 1. For Cycle 2, you will be randomly assigned (as in the flip of a coin) to 1 of 2 study groups. There is an equal chance of being assigned to either group: * If you are in Group A, you will receive rasburicase on Day 1 of Cycle 2. If the doctor thinks it is needed, you may also receive the drug on Days 2-5 of Cycle 2. * If you are in Group B, you will receive allopurinol by vein over 30 minutes each day on Days 1-5 of Cycle 2. Group B Participants: If your uric acid blood levels continue to increase in Cycle 2 and you show symptoms of tumor lysis syndrome, you may receive rasburicase as a single dose. If the doctor thinks it is needed, you may also receive 1 or more additional dose(s). Study Visits: On Day 1 of Cycle 1: * Blood (about 1 teaspoon) will be drawn to check uric acid levels before and 4 hours after you receive rasburicase. * Blood (about 2 tablespoons) will be drawn for routine tests. * Blood (about 1 teaspoon) will be drawn for antibody testing. Antibodies are proteins made by the body that the immune system uses to help prevent disease. On Days 2-5 of Cycle 1: * Blood (about 1 teaspoon) will be drawn to check uric acid levels. * Blood (about 2 tablespoon) will be drawn for routine tests. At the end of both cycles, blood (about 1 teaspoon) will be drawn for antibody testing. Length of Study: You will receive drugs on this study for up to 2 cycles. You will be taken off study if intolerable side effects occur. Your participation in the study will be over after the follow-up visit. Follow-Up: Three (3) months after the end of Cycle 2, blood (about 1 teaspoon) will be drawn for antibody testing. This is an investigational study. Allopurinol is commercially available and FDA approved to treat TLS. Rasburicase is commercially available and FDA approved for treating TLS for 1 cycle in patients with leukemia, lymphoma, and solid tumor cancers who are receiving anti-cancer therapy. It is investigational to give rasburicase for 2 cycles. Up to 55 patients will take part in this study. All will be enrolled at MD Anderson.