The goal of this clinical research study is to learn about the safety of giving a stem cell transplant from a tissue-mismatched donor, followed by cyclophosphamide, to patients with certain types of blood disorders or blood cancers. Melphalan, thiotepa, and fludarabine will also be given before the transplant.

Researchers will study the health status of these patients at 3 months after the transplant.

The Study Treatment:

Cyclophosphamide is designed to interfere with the multiplication of cancer cells, which may slow or stop their growth and spread throughout the body. This may cause the cancer cells to die.

In this study, researchers want to learn if cyclophosphamide can help to prevent graft-versus-host disease (GVHD -- when transplanted immune tissue, such as white blood cells, attacks the tissues of the recipient's body).

Melphalan, thiotepa, and fludarabine are commonly used in combination with a stem cell transplant.

Study Treatment Administration:

If you are found to be eligible to take part in this study, you will receive chemotherapy for 6 days:

• You will receive melphalan by vein over 30 minutes on Day -8 (8 days before the transplant).
• You will receive thiotepa by vein over 4 hours on Day -7.
• You will receive fludarabine by vein over 1 hour on Days -6, -5, -4, and -3.

If thiotepa is not available, you will receive melphalan by vein over 30 minutes on Day -6 and fludarabine by vein over 1 hour on Days -5, -4, -3, and -2. You will receive total body irradiation (TBI) on Day -1.

On Day 0, you will receive the donor's stem cells by vein. This may last anywhere from 15 minutes to several hours.

On Days 3 and 4, you will receive cyclophosphamide by vein over 3 hours. You will also receive mesna by vein over 30 minutes every 4 hours for a total of 10 mesna doses on Days 3 and 4. Mesna is given to lower the risk of side effects to the bladder.

Starting on Day 5, you will receive tacrolimus and mycophenolate mofetil (MMF) to help lower the risk of GVHD. Tacrolimus will be given by vein as a continuous infusion for about 2 weeks. After the 2 weeks of taking tacrolimus by vein, you will take tacrolimus by mouth as a pill for at least 3 months. MMF will be given by mouth, 3 times a day, usually until Day 35.

Starting on Day 7, you will receive filgrastim (G-CSF) once a day as an injection under the skin, until your blood cell counts reach a high enough level.

Depending on the type of disease that you have, your doctor may decide to give you rituximab by vein over several hours on Days -13, -6, 1, and 8. Rituximab is given to help the body get rid of abnormal white blood cells.

Length of Study Participation:

You will be in the hospital for about 4 weeks after the transplant. You will be taken off study if the disease gets worse. The study drugs will be stopped if intolerable side effects occur.

Follow-Up Visits:

You will be asked to stay close enough to Houston to be able to come back for any visits for at least 100 days after the transplant.

At 1, 3, 6, and 12 months after the transplant, the following tests and procedures will be performed:

• You will have a physical exam.
• Blood (about 4 tablespoons) will be drawn for routine tests.
• You will have a bone marrow biopsy/aspirate to check the status of the disease. If you have lymphoma or aplastic anemia, you may have a bone marrow biopsy/aspirate at 3, 6, and 12 months, if your doctor thinks it is needed.
• Blood (about 4 tablespoons) will be drawn to measure tumor cells and to predict graft failure and/or relapse.
• You may have urine collected and/or scans performed such as x-rays, CT scans, and/or a positron emission tomography (PET) scan. These scans and urine tests would only be done if the study doctor thinks they are needed to check the status of the disease.
• Blood (about 4 tablespoons) will be drawn to check your immune system.

If you have AML, at 2 months after the transplant, blood (about 4 tablespoons) will be drawn to check your immune system.

If you have MM, you will have a bone survey once a year.

If the study doctor thinks it is needed based on side effects you may be having, additional follow-up tests will be performed.

You may be contacted by phone 1-2 times a year to ask about the status of the disease. These calls will take about 10 minutes to complete.

This is an investigational study. All of the drugs used in this study are commercially available and FDA approved. However, it is investigational to give high-dose cyclophosphamide for preventing GVHD that may occur after a stem cell transplant from a tissue-mismatched donor.

Up to 337 patients will take part in this study. All will be enrolled at MD Anderson.

Inclusion Criteria:

1. Patients < 55 years (Myeloablative regimen #1) or > 55 and </= 75 years or significant comorbidities (Reduced intensity regimen #2) old lacking a matched related volunteer donor identified in time for transplant for which a related haploidentical donor (</= 7/8 allele match at the A, B, C, DR loci), a 7/8 allele matched related or unrelated donor is identified, or a matched unrelated donor (MUD). The patients must be diagnosed with a high-risk disease defined as following:
2. Acute lymphocytic leukemia (ALL) in CR1 with high-risk features including adverse cytogenetics such as t(9;22), t(1;19), t(4;11), or MLL gene rearrangements; ALL in second or greater remission or ALL with relapsed disease, peripheral blood blasts < 1000/microliter, ALL patients must show response to most recent received chemotherapy;
3. Acute myeloid leukemia (AML) in CR1 with intermediate-risk disease or high-risk features defined as: Greater than 1 cycle of induction therapy required to achieve remission; Preceding myelodysplastic syndrome (MDS) or myeloproliferative disease; Presence of FLT3 mutations or internal tandem duplications; FAB M6 or M7 classification; Adverse cytogenetics, -5, del 5q, -7, del7q, abnormalities involving 3q, 9q, 11q, 20q, 21q, 17, +8 [> 3 abnormalities], peripheral blood blasts <1000/microliter, AML patients must show response to most recent received chemotherapy;
4. AML in second or greater remission, primary induction failure and patients with relapsed disease, peripheral blood blasts <1000/microliter; patients > 55 years and </= 75 years need to be in morphologic remission at transplant (< 5% blasts).
5. Myelodysplastic syndrome (MDS) with International Prognostic Scoring System (IPSS) intermediate-2 or higher; or therapy-related MDS
6. Aplastic anemia with Absolute neutrophil count (ANC)<1000 and transfusion dependent after they failed immunosuppression therapy
7. Chronic myeloid leukemia (CML) >/=1st chronic phase, after failed >/=2 lines of tyrosine kinase inhibitors; in accelerated or blast phase with > 30% bone marrow blasts;
8. Prior allogeneic stem cell transplant more than 6 months from the first transplant, in remission.
9. Chemotherapy-sensitive relapsed lymphoma (Complete or partial response), Hodgkin's or non-Hodgkin's lymphoma, no evidence of "bulky" disease (> 10 cm in diameter);
10. Patients with chemo-sensitive CLL with persistent or recurrent disease after fludarabine-based regimens, no evidence of "bulky" disease (> 10 cm in diameter)
11. Patients with poor prognosis multiple myeloma by cytogenetics (del13, del 17p, t(1;14) or t(14;16) or hypodiploidy, with advanced disease (stage>/=2) and /or relapsed after autologous stem cell transplant.
12. Patients with myelofibrosis (Lille >0, transfusion dependency, progression to blast phase; however, in remission from AML) or chronic myelomonocytic leukemia (CMML). These patients will be treated with the reduced-intensity conditioning regimen #2 and will be subject to the same stopping rule as the group >/= 55 years or with comorbidities.
13. Zubrod performance status 0-1 or Lansky PS greater or equal to 70%.
14. Patients above >/=65 years old should have an age-adjusted co-morbidity index of </= 3.
15. Available donor able to undergo a bone marrow harvest. For matched unrelated donor transplants only: Peripheral blood stem cells may be collected if donor is unavailable for bone marrow harvest or if adequate bone marrow cannot be collected.
16. Bilirubin </= 1.5 mg/dl (unless Gilbert's syndrome), ALT or AST </= 200 IU/ml.
17. Serum creatinine clearance >/=50 ml/min (calculated with Cockcroft-Gault formula); Creatinine for children </=1.5 mg/dl or </=2 times upper limit of normal for age (whichever is less);
18. Diffusing capacity for carbon monoxide (DLCO) >/= 45% predicted corrected for hemoglobin. For pediatric patients, if unable to perform pulmonary function, >/= 92% oxygen saturation with pulse oximetry.
19. Left ventricular ejection fraction (LVEF) >/= 40%.
20. Patient or patient's legal representative, parent(s) or guardian should provide written informed consent. Assent of a minor if participant's age is at least seven and less than eighteen years.

Exclusion Criteria:

1. HIV positive; active hepatitis B or C
2. Patients with active infections. The PI is the final arbiter of the eligibility.
3. Liver cirrhosis with greater than grade 1 stage 1 inflammation/fibrosis
4. Uncontrolled central nervous system (CNS) involvement by tumor cells
5. Patients with AML must have less than 30% bone marrow blasts and no peripheral blood blasts.
6. History of another primary malignancy that has not been in remission for at least 3 years. (The following are exempt from the 3-year limit: non-invasive nonmelanoma skin cancer, fully excised melanoma in situ [Stage 0], curatively treated localized prostate cancer, and cervical carcinoma in situ on biopsy or a squamous intraepithelial lesion on PAP smear.)
7. Positive Beta human chorionic gonadotropin (HCG) test in a woman with child bearing potential defined as not post-menopausal for 12 months or no previous surgical sterilization.
8. Inability to comply with medical therapy or follow-up.