Inclusion Criteria:

          1. Histologically confirmed Multiple Myeloma prior to enrolment and randomization.

          2. At least 4 weeks (112 days) from last induction cycle of combination/multi-agent
             cyto-reductive chemotherapy and no single agent chemotherapy/maintenance within 7 days
             (e.g. lenalidomide, pomalidomide, bortezomib, dexamethasone, etc).

          3. Eligible for Autologous Hematopoietic stem cell transplantation according at the
             investigator discretion.

          4. The subjects should be in first or second CR (including CR and SCR) or PR (including
             PR and VGPR)

          5. Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1.

          6. Adequate organ function at baseline .

          7. Subjects must use effective contraception.

        Exclusion Criteria:

          1. Previous history of autologous or allogeneic-HCT

          2. Failed previous HSC collections or collection attempts.

          3. Patients whose apheresis product were to be further selected and purified

          4. Taken any of the listed below concomitant medications, growth factors or stimulating
             agents within the designated washout period:

               1. Dexamethasone: 7 days

               2. Thalidomide: 7 days

               3. Lenalidomide: 7 days

               4. Pamolidomide: 7 days

               5. Bortezomib: 7 days

               6. Carfilzomib: 7 days

               7. G-CSF: 14 days

               8. GM-CSF or Neulasta®: 21 days

               9. Combination/multi-agent cyto-reductive therapy

              10. Erythropoietin or erythrocyte stimulating agents: 30 days

              11. Eltrombopag, romiplostim or platelet stimulating agents: 30 days

              12. Carmustine (BCNU): 42 days/6 weeks

          5. Received >6 cycles lifetime exposure to Lenalidomide.

          6. Received >2 cycles of alkylating agent combinations.

          7. Received 3-bis(2-chloroethyl)-1nitrosourea (BCNU or Carmustine) within 6 weeks prior
             to anticipated first dose of G-CSF.

          8. Received prior treatment with radioimmunotherapy, (e.g. radionuclides, holmium).

          9. Received marrow stimulating factors:

               1. Received G-CSF within 14 days prior to anticipated first dose of G-CSF.

               2. Received Pegfilgrastim (GM-CSF or Nulesta) within 3 weeks prior to anticipated
                  first dose of G-CSF.

               3. Received erythrocyte of platelet stimulating agents within 30 days prior to
                  anticipated first dose of G-CSF

         10. Plans to receive maintenance treatment within 100 days post-engraftment (e.g.
             Lenalidomide, Bortezomib, Pomalidomide, Thalidomide, Carfilzomib, etc.)

         11. Has received a live vaccine within 30 days of the planned start of study therapy.
             Seasonal flu vaccines that do not contain live virus are permitted.

         12. Known active CNS metastases or carcinomatous meningitis.

         13. A history of allergic reactions attributed to compounds of similar chemical or
             biologic composition to BL-8040, G-CSF, or other agents used in the study.

        16. Has an active infection requiring systemic therapy or uncontrolled infection. Has a
        known additional malignancy that is progressing or requires active treatment. Has an
        underlying medical condition that would preclude study participation.

        17. Is currently participating and receiving study therapy or has participated in a study
        of an investigational agent and received study therapy or used an investigational device
        within 4 weeks of the first dose of treatment.

        18. O2 saturation < 92% (on room air). 19. History of unexplained syncope, syncope from an
        uncorrected cardiac etiology, or family history of sudden death.

        20. History or family history of Long QT Syndrome or Torsade de Pointes. Myocardial
        infarction, CABG, coronary or cerebral artery stenting and /or angioplasty, stroke, cardiac
        surgery, or hospitalization for congestive heart failure within 3 months or greater than
        Class 2 Angina Pectoris or NYHA Heart Failure Class >2. QTcF > 470 msec, PR > 280 msec,
        Mobitz II 2nd degree AV Block, 2:1 AV Block, High Grade AV Block, or Complete Heart Block,
        unless the patient has an implanted pacemaker or implantable cardiac defibrillator (ICD)
        with backup pacing capabilities.

        21. Has known psychiatric or substance abuse disorders that would interfere with
        cooperation with the requirements of the trial.

        22. Is pregnant or breastfeeding, or expecting to conceive or father children within the
        projected duration of the trial, starting with the screening visit through 30 days after
        the last dose of trial treatment.

        23. Has a known history of HIV (HIV 1/2 antibodies), active / chronic Hepatitis B or C.