Open-Label Study Designed to Evaluate the Safety and Preliminary Efficacy of ApoCell for the Prevention of Acute GvHD

Inclusion Criteria: Recipient 1. Adult male or female subjects, 18-60 years of age, inclusive, at the time of screening visit weighing at least 40 kg. 2. Subjects are eligible for allogeneic sibling HLA-matched HSCT for any disease for which transplantation is appropriate except progressive or poorly controlled malignancies. Only one of the following malignancies should be present: 1. Acute lymphoblastic leukemia or acute myeloid or undifferentiated or biphenotypic, leukemia, in complete remission or beyond but with ≤10% blasts in bone marrow. 2. Acute myeloid leukemia in complete remission if it has evolved from myelodysplastic syndrome (MDS) (there should be documented diagnosis of MDS at least 3 months prior to diagnosis of acute myeloid leukemia). 3. Myelodysplastic syndromes - MDS 4. Therapy related MDS (irrespective of IPSS). 5. Chronic myeloid leukemia (CML) chronic phase-1 (imatinib failures, imatinib intolerance), or any CML beyond first chronic phase. 6. Multiple Myeloma. 3. The donor and recipient must have at least a 7/8 HLA match at the HLA A, B, C, and DR loci. 4. Life expectancy of at least 6 months at the time of the baseline visit. 5. Karnofsky performance status score ≥ 80% at time of the screening visit. 6. Cardiac left ventricular ejection fraction ≥ 40% in adults within 4 weeks of initiation of conditioning; required if prior anthracycline exposure or history of cardiac disease. 7. Pulmonary function test with DLCO, FEV1 and FVC of ≥ 60%. 8. Oxygen saturation ≥ 90% on room air. 9. Subjects must have normal organ function as defined below: 1. AST (SGOT)/ALT (SGPT) ≤ 2.5 x upper limit of normal (ULN). 2. Serum creatinine \<2.5 mg/dL. 3. Serum bilirubin \<3 mg/dL. 4. Coagulation markers - PT and PTT within normal limits. 10. Signed written informed consent to participate in the study independently by subject. Subjects requiring a guardian to sign informed consent will not be included. 11. Ability to comply with the requirements of the study. 12. If female, agree to use an acceptable method of birth control or be surgically sterile, and have a negative pregnancy test regardless of child-bearing potential. Exclusion Criteria: recipient 1. Participation in an investigational trial within 30 days of the screening visit. 2. Have progressive or poorly controlled malignancies. 3. T-cell depleted allograft. 4. Uncontrolled infections including sepsis, pneumonia with hypoxemia, persistent bacteremia, or meningitis within two weeks of the screening visit. 5. Current known acute or chronic infection with HBV or HCV. 6. Known human immunodeficiency virus (HIV) infection or AIDS. 7. Subjects with severe or symptomatic restrictive or obstructive lung disease or respiratory failure requiring ventilator support. 8. Subjects with other concurrent severe and/or uncontrolled medical condition which could compromise participation in the study (i.e. active infection, uncontrolled diabetes, uncontrolled hypertension, congestive cardiac failure, unstable angina, ventricular arrhythmias, active ischemic heart disease, myocardial infarction within six months, chronic liver or renal disease, active upper gastrointestinal tract ulceration). 9. Any chronic or acute condition susceptible of interfering with the evaluation of investigational product effect. 10. Any form of substance abuse (including drug or alcohol abuse), psychiatric disorder or any chronic condition susceptible, in the opinion of the investigator, of interfering with the conduct of the study. 11. Organ allograft or previous history of allogeneic stem cell transplantation. 12. For all women: A positive pregnancy test at screening or breast-feeding. 13. Subjects who are likely to be non-compliant or uncooperative during the study. Inclusion criteria: Donor 1. Male or female donors, 18 - 65 years of age, inclusive. 2. The donor and recipient must have at least a 7/8 HLA match at the HLA A, B, C, and DR loci. 3. Above 40 kg. 4. Not pregnant and negative pregnancy test. 5. Serum creatinine \< 2.5 mg/dL. 6. Oxygen saturation ≥ 90% on room air. 7. No severe or symptomatic restrictive or obstructive lung disease or respiratory failure requiring ventilator support. 8. No uncontrolled hypertension or congestive heart failure, active angina pectoris requiring the use of nitrates, or major ventricular arrhythmia or cardiac failure requiring active treatment. 9. Not HIV-1/2 or HTLV I/II seropositive or evidence of acute CMV infection. 10. Not seropositive for Hepatitis B or C. 11. Not positive for syphilis. 12. No known bone marrow disease. 13. No significant organ dysfunction. 14. No acute infectious disease within two weeks of donation. 15. Willingness to donate hematopoietic blood mononuclear cells for the generation of ApoCell more than one time if required and in addition to the donation for the HSCT. 16. Ability to provide written informed consent and comply with study requirements.