The following criteria is provided for health care professionals.

Inclusion Criteria (DONOR):

• Age 18 to 70 years of age.
• ECOG performance status of 0 or 1.
• PART 1: Donor must be a 5/6 or 6/6 HLA-matched sibling willing to donate PBSC for transplant.
• PART 2: Donor must be a 5/6 or 6/6 HLA-matched sibling or 3/6 or 4/6 HLA haploidentical donor willing to donate PBSC for transplant. Haploidentical donors will be allowed to participate upon investigator decision and based on the data reached from 5/6 or 6/6 HLA matched transplant done during Part 1 of the study.
• Adequate organ function defined by:
  • serum creatinine within normal limits or a minimum creatinine clearance (CrCl) value of ≥ 60 ml/min calculated using the Modification of Diet in Renal Disease (MDRD) Study equation
  • AST, ALT and total bilirubin ≤ 2x institutional upper limit of normal.
• Women of childbearing potential and men must agree to use adequate contraception with two different forms, including one barrier method, during participation in the study and for 2 weeks following dosing with BL-8040. Abstinence is acceptable if this is the established and preferred contraception for the subject.
• Female subjects must have a negative urine or serum pregnancy test within 72 hours prior to taking study medication if of childbearing potential or must be of non-childbearing potential. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. The serum pregnancy test must be negative for the subject to be eligible. Non-childbearing potential is defined as:
  • -≥ 45 years of age and has not had menses for > 2 years
  • Amenorrheic for > 2 years without a hysterectomy and oophorectomy and a FSH value in the postmenopausal range upon pretrial (screening) evaluation
  • Post-hysterectomy, oophorectomy, or tubal ligation. Documented hysterectomy or oophorectomy must be confirmed with medical records of the actual procedure or confirmed by an ultrasound. Tubal ligation must be confirmed with medical records of the actual procedure.
• Able and willing to comply with the requirements of the protocol.
• Able to understand and willing to sign an IRB-approved written informed consent document.

Inclusion Criteria (RECIPIENT):

• Age 18 to 75 years
• ECOG performance status of 0-2 (inclusive)
• One of the following diagnoses:
  • Acute myelogenous leukemia (AML) in 1st or subsequent remission
  • Acute lymphoblastic leukemia (ALL) in 1st or subsequent remission
  • Chronic myelogenous leukemia (CML) in chronic or accelerated phase
  • Non-Hodgkin lymphoma (NHL) or Hodgkin's disease (HD) in 2nd or greater complete remission, partial remission
  • Chronic lymphocytic leukemia (CLL)
  • Multiple myeloma (MM)
  • Myelodysplastic syndrome (MDS)
  • Myeloproliferative neoplasm (MPN) excluding primary or secondary myelofibrosis
• Adequate organ function defined by:
  • a creatinine clearance (CrCl) value of ≥ 60 ml/min
  • AST, ALT and a total bilirubin ≤ 2x institutional upper limit of normal.
• Adequate cardiac function with a left ventricular ejection fraction ≥ 40%.
• Adequate pulmonary function defined as NO severe or symptomatic restrictive or obstructive lung disease, and formal pulmonary function testing showing an FEV1 ≥50% of predicted and a DLCO ≥ 40% of predicted, corrected for hemoglobin.
• Women of childbearing potential and men must agree to use adequate contraception with a highly effective method (hormonal or barrier method of birth control, abstinence) prior to study entry and for the duration of study participation. Abstinence is acceptable if this is the established and preferred contraception for the subject.
• Female subjects must have a negative urine or serum pregnancy test within 72 hours prior to start of conditioning if of childbearing potential or be of non-childbearing potential. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. The serum pregnancy test must be negative for the subject to be eligible. Non-childbearing potential is defined as:
  • Amenorrheic for > 2 years without a hysterectomy and oophorectomy and a FSH value in the postmenopausal range upon pretrial (screening) evaluation
  • Post-hysterectomy, oophorectomy, or tubal ligation. Documented hysterectomy or oophorectomy must be confirmed with medical records of the actual procedure or confirmed by an ultrasound. Tubal ligation must be confirmed with medical records of the actual procedure.
• ≥ 45 years of age and has not had menses for > 2 years
• Able to understand and willing to sign an IRB-approved written informed consent document.

Exclusion Criteria (DONOR):

• Received any investigational agent within 30 days and/or 5 half-lives (of the other investigational agent), whichever is longer, of receiving BL-8040.
• Active HIV or hepatitis B or C infection
• Pregnant or breastfeeding.
• Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements.
• Known allergy or hypersensitivity to any of the test compounds, materials, or contraindication to test products.
• Any malignancies in the 2 years prior to baseline, excluding: basal cell carcinoma, in situ malignancy, low-risk prostate cancer, cervix cancer after curative therapy.
• A comorbid condition which, in the view of the investigators, renders the subject at high risk from treatment complications.

Exclusion Criteria (RECIPIENT):

• Recipient must not have received any investigational drug within 30 days and/or 5 half-lives (whichever is longer) of starting conditioning treatment.
• Pregnant or breastfeeding.
• Active HIV or hepatitis B or C infection.
• Any medical condition which, in the opinion of the clinical investigator, would interfere with the evaluation of the patient. Subjects with a clinically significant or unstable medical or surgical condition or any other condition that cannot be well-controlled by the allowed medications permitted in the study protocol that would preclude safe and complete study participation, as determined by medical history, physical examinations, ECG, laboratory tests, or chest-X-ray and according to the investigator's judgment.