Inclusion Criteria:

1. Informed consent obtained before any trial-related activities. (Trial-related activities are any procedure that would not have been performed during normal management of the subject.)
2. Bone marrow plasmacytosis > 10% (as determined by bone marrow aspirate) or plasmacytoma
3. Relapse or progression after at least one prior systemic treatment regimen for MM as evidenced by ≥ 25% increase in the M-protein as compared to the best response from the previous treatment regimen.

3a. One prior therapy for multiple myeloma, Measurable disease, as defined by persistent presence of serum and/or urine monoclonal protein or abnormal serum free light chain ratio following the prior treatment.

a. Only for the last seven patients enrolled into the cohort 7 or MTD. 4. Full recovery from acute toxicities of prior anti-MM therapies. 5. Peripheral blood NK cells (Absolute CD16, 56)≥ 0.05 x 109/L (50/mm3) 6. Detectable binding of Anti-KIR (1-7F9) to subject NK cells 7. Age ≥ 18 years 8. Eastern Cooperative Oncology Group (ECOG) performance status of 0,1 or 2 9. Clinical laboratory values at screening:

• serum creatinine < grade 2 toxicity i.e. 1.5x upper limit of institutional normal value
• total bilirubin < 1.5x upper limit of institutional normal value
• AST < or = 3x upper limit of institutional normal value
• ANC>1.2 x109/L
• Platelets >70x109/L

Exclusion Criteria:

1. Known or suspected allergy to trial product or related products
2. Previous participation in this trial (dosed)
3. Females of childbearing potential who are pregnant, breast-feeding or intend to become pregnant or are not using adequate contraceptive methods (appropriate methods include abstinence and the following methods: diaphragm, condom (by the partner), intrauterine device, sponge, spermicide or oral contraceptives)
4. Male subjects who are sexually active and have not been surgically sterilized must be informed that they must either use a condom during intercourse, ensure that their partners practices contraception, or they must refrain from sexual intercourse during the study and until 1 month after completion of the trial.
5. Use of an investigational agent within 30 days of the first dose of study drug (or five half-lives of any antibody).
6. Current treatment with any other anti-MM therapy excluding prophylactic bisphosphonates.
7. Radiotherapy against bone lesions within 4 weeks or visceral lesions within 8 weeks of Screening.
8. Thalidomide or bortezomib treatment within 14 days of Screening.
9. Cytotoxic chemotherapy (excluding thalidomide or bortezomib) or corticosteroid treatment within 28 days of Screening.
10. Subjects with non-secretory multiple myeloma
11. Subjects on dialysis
12. Use of myeloid growth factor within 28 days of screening
13. G-CSF treatment within 28 days of screening
14. Active autoimmune disease
15. Active infectious disease (e.g. HIV, chronic hepatitis, etc.) as judged by the investigator.
16. New York Heart Association (NYHA) class III-IV heart failure
17. Severe neurological / psychiatric disorder as judged by the investigator
18. Clinical evidence of an active second malignancy, with the exception of basal cell carcinoma or in situ carcinoma of cervix.
19. Subjects with a history of allogenic transplantation.
20. Subject who have undergone autologous transplantation within the last 3 months.
21. Mental incapacity or inadequate understanding of English.
22. Any serious medical condition that in the opinion of the investigator, disqualifies the subject for inclusion in the trial.