Inclusion Criteria:

• Relapsed or refractory multiple myeloma treated with at least 1 and not more than 3 prior regimens. Prior therapy with bortezomib is allowed if there has been no relapse or progression within 3 months of the last dose of bortezomib, and bortezomib is considered by the treating physician to be a reasonable therapy for the patient.
• Monoclonal protein in the serum of ≥ 1 g/dL (10 g/L) or monoclonal light chain in the urine protein electrophoresis of ≥ 200 mg/24 hours, involved SFLC level ≥ 10 mg/dL (100 mg/L) provided SFLC ratio is abnormal, or measurable plasmacytoma.
• Are ≥ 18 years of age.
• Have given written informed consent prior to any study-specific procedures

• Have adequate organ function including:

  • Absolute neutrophil count (ANC) ≥ 1000/microliter
  • Platelet (PLT) count ≥ 75,000/microliter
  • Hemoglobin (Hgb) ≥ 8.0 g/dL
  • Total bilirubin ≤ 1.5 x upper limit of normal (ULN) (if total is elevated check direct and, if normal, patient is eligible)
  • Aspartate transaminase (AST) ≤ 3 x ULN
  • Creatinine ≤ 1.7 x ULN
• Have a performance status of ≤ 2 on the Eastern Cooperative Oncology Group (ECOG) scale (refer to Attachment JDCF.5).
• Have discontinued all previous therapies for cancer, including chemotherapy and radiotherapy at least 2 weeks (6 weeks for mitomycin-C or nitrosoureas) prior to study enrollment and recovered from the acute effects of therapy.
• Are reliable and willing to make themselves available for the duration of the study and are willing to follow study procedures.
• Males and females with reproductive potential must agree to use medically approved contraceptive precautions during the trial and for 4 months following the last dose of study drug.
• Females with child bearing potential must have had a negative urine or serum pregnancy test ≤ 3 days prior to the first dose of study drug.
• Have an estimated life expectancy of ≥ 16 weeks.
• Treatment with prior autologous transplant is permitted. If a transplant is used as consolidation following chemotherapy, without intervening disease progression, it will be considered one line of treatment with the preceding chemotherapy.

Exclusion Criteria:

• Have received treatment within 30 days of the initial dose of study drug with a drug that has not received regulatory approval for any indication.
• Have one or more serious preexisting medical conditions that, in the opinion of the investigator, would preclude participation in this study.
• Have uncontrolled infection.
• Females who are pregnant or lactating.
• Have known positive test results in human immunodeficiency virus (HIV), hepatitis B surface antigen (HBSAg), or hepatitis C antibodies (HCAb).
• Have peripheral neuropathy of > Grade 2, or of any grade with pain, as measured by CTCAE v3.0.
• Previously treated with LY2127399, or have had significant allergy to humanized monoclonal antibodies that, in the opinion of the investigator, poses an increased risk to the patient.
• Prior allogeneic hematopoietic stem cell transplant.
• Prior therapy with experimental agents targeting BAFF.
• Have QTc interval > 450 msec on baseline 12-lead ECG.