Infusion of Allogeneic CD19-Specific T Cells From Peripheral Blood

Gene Transfer: Gene transfer involves drawing blood from a transplant donor, and then separating out the T-cells using a machine. Researchers then perform a gene transfer to change the T-cells' DNA, and then inject the changed T-cells into the body of the patient receiving the transplant. This process is called a modified donor lymphocyte infusion (DLI). Study Groups: If you are found to be eligible to take part in this study, you will be assigned to 1 of 4 study arms, based on your age, treatment schedule, and disease status: * Participants in Arm 1 will receive the T-cells by vein about 6-12 weeks after the stem cell transplant. (Adults participants only) * Participants in Arm 2 will receive the T-cells by vein if, at any point, the disease comes back after stem cell transplant. Your doctor may decide that you need to receive chemotherapy before you are given the T-cells, in order to clear out the T-cells that are in your body already. This may help the infused T-cells work better. If more chemotherapy is needed, you will sign another informed consent document, which will the chemotherapy and its risks in detail. (Pediatric and adult participants eligible) * Participants in Arm 3 will receive the T-cells by vein about 6-12 weeks after the stem cell transplant. (Pediatric participants \[ages 1-17\] only) * Participants in Arm 4 will be given the T-cells as a scheduled infusion or if the disease comes back. This group is also scheduled to receive a stem cell transplant from a mismatched family member donor. (Pediatric and adult participants eligible) Once you have been assigned to a study arm, you will be assigned to 1 of 4 dose levels of genetically-changed T-cells, based on when you joined this study. The first group of participants will receive the lowest dose of T-cells, and each new group will receive a higher dose of changed T-cells than the group before it, as long as no intolerable side effects were seen. Chemotherapy and HSCT: After your donor's stem cells have been successfully collected, you will be admitted to the hospital to receive chemotherapy and the HSCT. These procedures are not considered part of this research study. You will discuss these procedures with a study doctor and sign an informed consent document with specific details of the HSCT procedure and possible risks, at another time. The T-cell Infusion: After the HSCT, the study chair will decide when you will be eligible for the T-cell infusion. You must be at least 42 days past your transplant without any serious evidence of active graft versus host disease (GVHD). GVHD occurs when donor cells attack the cells of the person receiving the transplant. Before the infusion, you will receive drugs to lower your risk of allergic reaction to the T-cells. Tylenol® (acetaminophen) will be given by mouth, and Benadryl® (diphenhydramine) may be given by mouth or by vein over a few minutes. The T-cell infusion is given by vein, usually over 15-30 minutes. During the infusion, your vital signs will be checked. The infusion may be given on one day, or it may be divided into two parts at least 24 hours apart. The first part of the infusion will be a much smaller part to ensure that you have no immediate side effects. Before the T cell infusion, you will receive drugs to lower your risk of allergic reaction to the T cells. Acetaminophen (Tylenol®) will be given by mouth, and diphenhydramine (Benadryl®) will be given by vein over a few minutes. If your cancer returns after the transplant, you may receive an additional T-cell infusion. If you receive an additional T-cell infusion, the screening tests will be repeated. The study doctor will discuss the results of the repeated screening tests with you. If the screening tests show that you are not eligible to receive the additional T-cell infusion, other treatment options will be discussed with you. Study Tests: Within 3 days after the T-cell infusion, and then about 1 week, 2 weeks, 4 weeks, 8 weeks, 3 months, 6 months and 12 months after the T-cell infusion, the following tests will be performed: * You will have a physical exam, including measurement of your height, weight, and vital signs. * Your medical history will be recorded. * Blood (about 4 tablespoons each time) will be drawn for research tests to check the level of the infused T-cells and to measure the number of B-cells and other (non-transplanted) T-cells. * Blood (about 4 tablespoons each time) will be drawn for routine tests and tests of your blood chemistry, and blood sugars. During the 4 week, 8 week, 3 month, 6 month, and 12 month visits, part of this blood sample will be used for tests of certain protein levels. During the Month 3 visit, part of this blood sample will be used to check for HAMA immune system reactions. If you leave the study before the Month 3 visit, blood (about 1 tablespoon) may be collected for HAMA immune system reaction testing, if possible. * You will have be checked for possible reactions to your treatment, including GVHD and graft failure. Graft failure occurs when donor cells may not be able to grow and multiply in your body. If this happens, there will be a high risk of infections and/or bleeding. If the number of white blood cells does not get back to high enough levels within 3 weeks after the transplant, more blood stem cells from the stem cell donor may be given. * You may need a skin biopsy or an endoscopy to check for GVHD and/or graft failure, as well. To collect a skin biopsy, the biopsy area is numbed with anesthetic, and a small amount of skin is collected using a needle or scalpel. An endoscopy is an exam where you will be mildly sedated to allow a thin, flexible, lighted tube, called an endoscope, to be inserted inside the esophagus, stomach, and first part of the small intestine. This will allow the doctor to look for abnormal areas that might not be so easily seen in x-rays. Within 3 months after the T-cell infusion, you will have CT scans and/or a bone marrow biopsy to check the status of the disease. An extra sample of bone marrow aspirate (about 2 teaspoons each time) will be drawn for research tests whenever a bone marrow aspirate/biopsy is being done if possible. These samples will be used for research tests to study how your immune system responds to the infusion of T-cells. To collect a bone marrow aspirate, an area of the hip is numbed with anesthetic, and a small amount of bone marrow is withdrawn through a large needle. Length of Study: You may continue taking part in this study for up to 3 months. You will be taken off study if the disease gets worse, you have any infections, or intolerable side effects occur. Your participation on this study will be over once you have completed the planned study visits at 3 months after the T-cell infusion. Retreatment: If you are taken off study because the disease got worse, you may be able to enroll on study again once the highest tolerated dose of T-cells is found. If this happens, you will follow the same schedule for dosing and study tests as described above. Long-Term Follow-Up: For safety reasons, the U.S. Food and Drug Administration (FDA) requires that patients who receive infusions of stem cells treated with a gene transfer procedure must have long-term follow-up for at least 15 years after receiving the gene transfer. This is an investigational study. The gene transfer or DLI (infusion with genetically-changed T-cells) are not commercially available or FDA approved for use in this type of disease. Their use in this study is considered investigational. The donor's leukapheresis procedure to collect cells for the manufacture of changed T-cells will be provided at no cost to you while you are on study. Up to 140 patients (and up to 140 donors) will take part in this study. All will be enrolled at MD Anderson.