This multicenter, open-label, dose-escalating study will assess the safety and efficacy of DFRF4539A in patients with relapsed or refractory multiple myeloma. Cohorts of patients will receive multiple ascending doses of intravenous DFRF4539A every 3 weeks or weekly. Patients exhibiting acceptable safety and evidence of clinical benefit may receive DFRF4539A for up to 17 cycles. Anticipated time on study treatment is 1 year or until disease progression or unacceptable toxicity occurs.

Inclusion Criteria:

• Adult patients; >/= 18 years of age
• Eastern Cooperative Oncology Group (ECOG) performance status 0, 1, or 2
• Relapsed or refractory multiple myeloma for which no effective standard therapy exists
• One of the prior therapies must have included a proteosome inhibitor or an immunomodulatory drug
• Measurable disease as defined by protocol

Exclusion Criteria:

• Prior use of monoclonal antibody within 4 weeks before Cycle 1, Day 1
• Treatment with radiotherapy, thalidomide, lenalidomide, bortezomib, any chemotherapeutic agent, or treatment with any investigational anti-cancer agent within 2 weeks prior to Cycle 1, Day 1
• Toxicities from any previous treatment must be resolved prior to Cycle 1, Day 1, except for neuropathy
• Completion of autologous stem cell transplant within 100 days prior to Cycle 1, Day 1
• Prior allogeneic stem cell transplant
• History of severe allergic or anaphylactic reactions to monoclonal antibody therapy (or recombinant antibody-related fusion proteins)
• Grade > 1 peripheral neuropathy
• Active infection at screening or any major episode of infection requiring treatment with IV antibiotics or hospitalization within 4 weeks prior to Cycle 1, Day 1
• Positive for hepatitis B, hepatitis C or HIV infection
• Pregnant or lactating women or women who intend to become pregnant within the period of time of this study