Any time the words "you," "your," "I," or "me" appear, it is meant to apply to the potential participant.

T-cells are white blood cells that are important to the immune system. The T cells for this study (called regulatory T-cells, or Tregs) will be from a donor who is not related to you. Before the Tregs are given to you, they may be changed in the laboratory to make use of sugar that is found in small amounts in blood cells through a process called fucosylation. They are then called fucosylated Tregs. Adding more sugars to the Tregs in the laboratory is designed to help the Tregs find their way faster to the bone marrow, which may help low blood counts to recover faster.

The goal of this clinical research study is to learn if it is safe and practical to give fucosylated Tregs to patients who will receive a matched related donor (MRD), a matched unrelated donor (MUD), or cord blood transplant. Researchers also want to learn if these Tregs may prevent or reduce the effects of graft-versus host disease (GVHD). GVHD can result from a reaction of the transplanted cord blood cells against certain tissues in the body.

This is an investigational study. Fucosylation of Tregs is not an FDA-approved process. It is currently being used for research purposes only. Fludarabine, melphalan, cyclophosphamide and rituximab are FDA approved and commercially available to be given to patients with leukemia or lymphoma having a cord blood transplant. Total body irradiation is delivered using FDA-approved and commercially available methods.

Up to 47 patients will take part in this study. All will be enrolled at MD Anderson.

Central Venous Catheter Placement:

You will first have a central venous catheter (CVC) placed. A CVC is a sterile flexible tube that will be placed into a large vein while you are under local anesthesia. Your doctor will explain this procedure to you in more detail, and you will be required to sign a separate consent form for it.

The chemotherapy, some of the other drugs in this study, the Tregs, and the MRD, MUD or cord blood transplant will be given by vein through your CVC. Some blood samples will also be drawn through your CVC. The CVC will remain in your body for about 2-5 months.

Study Treatments:

If you are found to be eligible to take part in this study, you will be assigned to a dose level of Tregs based on when you joined this study. You may receive fucosylated or non-fucosylated Treg cells. Two dose levels of fucosylated Tregs will be tested. Up to 3 participants will be enrolled in Dose Level 1, and up to 17 will be in Dose Level 2. The first group of participants will receive the lower dose level. The next group will receive a higher dose than the first group, if no intolerable side effects were seen.

The next 10 participants will receive non-fucosylated Tregs at Dose Level 2.

The last 34 patients enrolled in the study will be will be randomly assigned (as in the flip of a coin) to 1 of 2 study groups and will have an equal chance of receiving either fucosylated or non-fucosylated Treg cells.

You will receive 1 of 2 preparative regimens before your transplant. These regimens are used to prepare your body to receive the transplant. Your study doctor will decide which regimen is best for you.

Regimen #1:

On Day -12, you will receive rituximab by vein over 4-6 hours, if you are receiving it. This will depend on the disease that you have.

On Day -9, you will be admitted to the hospital and given fluids by vein to hydrate you.

On Day -8, you will receive fludarabine and cyclophosphamide by vein over 1 hour. You will also receive mesna by vein over 30-60 minutes before the cyclophosphamide dose and then every 4 hours for a total of 5 doses. Mesna is given to lower the risk of side effects to the bladder caused by cyclophosphamide.

On Days -7, -6, and -5, you will receive fludarabine by vein over 1 hour.

On Day -4, you will receive a single treatment of low-dose total body irradiation as part of the standard of care for stem cell transplants. You will receive a separate consent form that describes this procedure and its risks.

On Day -1, you will receive the Tregs by vein over 30-60 minutes.

On Day 0, you will receive your stem cell transplant through the CVC over about 30 minutes to several hours depending on the donor type of stem cell transplant you receive.

Regimen #2:

On Day -12, you will receive rituximab by vein over 4-6 hours, if you are receiving it. This will depend on the disease that you have.

On Day -6, you will be admitted to the hospital and given fluids by vein to hydrate you.

On Days -5, -4, -3 and -2, you will receive fludarabine by vein over 1 hour.

On Day -2, you will receive melphalan by vein over 30 mins.

On Day -1, you will receive the Tregs by vein over 30-60 minutes.

On Day 0, you will receive your stem cell transplant through the CVC over about 30 minutes to several hours depending on the donor type of stem cell transplant you receive.

Supportive Drugs:

You will be given standard drugs to help decrease the risk of side effects. You may ask the study staff about how the drugs are given and their risks.

Starting on Day -3, you will receive sirolimus by mouth once a day. You will receive mycophenolate mofetil (MMF) as a tablet by mouth 3 times a day.

If you are not able to take the MMF tablet by mouth, you will receive MMF by vein over 2 hours. If you do not have GVHD at Day 100, the dose of MMF will be gradually lowered. If you have GVHD, MMF may be stopped 7 days after the GVHD is controlled. If you do not have GVHD at Day 180 after your transplant, the dose of sirolimus will be gradually lowered. Your doctor will discuss this with you.

You will receive filgrastim as an injection under the skin 1 time a day, starting on Day 0 for cord blood transplant or Day 7 for a matched related or MUD transplant, until your blood cell levels return to normal. Filgrastim is designed to help with the growth of white blood cells.

Study Visits:

As part of standard care, you will remain in the hospital for about 4 weeks after the transplant. After you are released from the hospital, you will continue as an outpatient in the Houston area to be monitored for infections and transplant-related complications.

On Days -10, -1, 0, +1, +3, +7, +14, +21, and then at 1, 2, 3, 6, and 12 months after the transplant, blood (about 3 tablespoons) will be drawn to check your immune function, response to the T cells, inflammatory responses, and for GVHD markers. If possible, the blood will be collected during standard of care blood draws so that no additional needle sticks will be needed.

About 1, 3, 6, and 12 months after the transplant:

• You will have a physical exam.
• You will be checked for possible reactions to the transplant and study drugs, including GVHD.
• Blood (about 4 teaspoons) will be drawn for routine tests, to check for cytomegalovirus (CMV), and for genetic tests to learn if your body has accepted the donor cells.

Urine will be collected for routine tests.

• If the doctor thinks it is needed, you will have a bone marrow aspiration to check the status of the disease. To collect a bone marrow aspiration/biopsy, an area of the hip or other site is numbed with anesthetic, and a small amount of bone marrow and bone is withdrawn through a large needle.
• If you have lymphoma or Hodgkin's Disease and the doctor thinks it is needed, you will have a CT scan of your neck, chest, abdomen, and pelvis to check the status of the disease.

Length of Study:

You will be on study for up to 1 year. You will be taken off study early if the disease gets worse, if intolerable side effects occur, if not enough T cells can be created, if you are unable to follow study directions, or if your doctor thinks it is in your best interest.

Inclusion Criteria:

1. Patients with high risk hematologic malignancies, including those with induction failure and in relapse.
2. Patients must have matched related or matched unrelated donor source OR CB unit(s) available for the primary transplant which is/are matched with the patient at 4, 5, or 6/6 HLA class I (serological) and II (molecular) antigens. The cord(s) must contain at least 3 x 107 total nucleated cells/Kg recipient body weight (pre-thaw).
3. Age Criteria: Age >/= 18 and </= 80 years old. Eligibility for pediatric patients will be determined in conjunction with an MDACC pediatrician.
4. Bilirubin </= 1.5 mg/dl, SGPT </= 200 IU/ml (unless Gilbert's syndrome).
5. Calculated creatinine clearance of >50 mL/min using the Cockcroft-Gault equation for adult patients 18 to 70 years old based on ideal body weight.
6. Diffusing capacity for carbon monoxide (DLCO) >/= 45% predicted corrected for hemoglobin. For children </= 7 years of age who unable to perform the pulmonary function test, an O2 saturation of >/= 92% on room air.
7. Left ventricular ejection fraction (LEF) >/= 40%.
8. Zubrod performance status </= 2 or Lansky of >/= 60%.
9. Twenty-one or more days must have elapsed since the patient's last radiation or chemotherapy administration before beginning treatment for stem cell transplant. Hydrea, Gleevec and other TKI inhibitors as well as intrathecal therapy are accepted exceptions.
10. A back-up graft identified, in case of graft failure, from any of the following sources: an available fraction of autologous marrow; or PBPCs harvested and cryopreserved; or family member donor; or a third cord blood unit.
11. Able to stop all CYP3A4 inhibitors (voriconazole or posaconazole) at least 7 days before admission.

Exclusion Criteria:

1. HIV seropositivity.
2. Uncontrolled infection, not responding to appropriate antimicrobial agents after seven days of therapy. The PI is the final arbiter of eligibility.
3. Positive beta HCG in female of child-bearing potential defined as not post-menopausal for 12 months or no previous surgical sterilization or lactating females.
4. Unable to sign informed consent.