Eligibility Criteria:
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 10 days 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.
* 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 by MDRD study equation
* 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.
* Female subjects must have a negative urine or serum pregnancy test 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:
\*≥ 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.
* 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 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.