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.