A Phase 1 Safety Study of LY2127399 in Combination With Bortezomib

Inclusion Criteria: * Have relapsed or refractory multiple myeloma treated with at least 1 prior regimen. 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. * Have measurable disease defined by one or more of the following: * Monoclonal protein in the serum of ≥1 g/dL (10 g/L). * Monoclonal light chain in the urine protein electrophoresis of ≥ 200 mg/24 hours. * Involved Serum Free Light Chain (SFLC) level \> 10 mg/dL (100 mg/L) provided SFLC ratio is abnormal. * 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 ≥ 50,000/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 ≤ 3.0 mg/dl. * 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.