Inclusion Criteria:

• Able to provide signed, informed consent;
• Male or female, >/= 18 years old;
• Multiple myeloma with one or more criteria for measurable disease (serum M protein > 0.5 gm/dl, urinary M protein excretion > 200 mg/24 hours, serum free light chain measurement >20 mg/dl,);
• Refractory or relapsed to at least two prior standard systemic anti-myeloma treatment regimens one of which must include either thalidomide, lenalidomide or bortezomib;
• Adequate performance status (Karnofsky Scale >/= 70%);
• Life expectancy at least 6 months;
• Adequate cardiac function: MUGA scan or 2D-ECHO with LVEF 55%, EKG with no medically relevant arrhythmia uncontrolled on medications;
• Adequate hematologic status within 2 weeks before study drug administration:
• Hemoglobin >/=8.0 g/dL and platelets >/=75,000/mm3 (both without transfusion or other hematologic support within 7 days of laboratory testing)
• White blood count (WBC) >/= 2,000/mm3and absolute neutrophil count (ANC) >/=1,500/mm3 (both without the use of colony stimulating factors within 7 days of laboratory testing);
• Adequate renal function: serum creatinine </+ 2.5 mg/mL;
• Adequate hepatic function
• AST and ALT </= 2.5 x the ULN
• Total bilirubin </= 1.5 x the ULN

Exclusion Criteria:

• 1. Pregnant or lactating women. Women of childbearing potential must have a negative pregnancy test Pregnancy testing is not required for post-menopausal or surgically sterilized women;
• Patients who are eligible for stem cell transplant.
• Women of childbearing potential and fertile men who are not practicing or who are unwilling to practice birth control while enrolled in the study until at least 12 weeks after the last hLL1-dox infusion;
• Prior local radiotherapy within 14 days; chemotherapy or kyphoplasty within 21 days, immunotherapy, plasmapheresis, or major surgery within 28 days; prior stem cell transplant within 12 weeks.
• Must have no persistent ≥ Grade 2 toxicity from prior treatments;
• Prior treatment with any other therapeutic agents for MM or investigational agents within 4 weeks, unless off study, and agreed by Sponsor;
• A history of allergic or adverse reactions to anthracycline/anthracenedione agents;
• Cumulative life-time anthracycline/anthracenedione exposure exceeding 300 mg/m2 (including daunorubicin, idarubicin, epirubicin or mitoxantrone);
• Known to be HIV positive, or any prior hepatitis B or C infection;
• Any history of clinically significant autoimmune disease (e.g., collagen vascular disorders, autoimmune hepatitis, Coombs positive anemia/thrombocytopenia, etc.)
• Prior history of mediastinal or pericardial external beam radiation therapy.
• Prior history of treatment with trastuzumab, unless discussed with and agreed to by Medical Monitor.
• Systemic infection or requiring anti-infectives within 7 days before first dose of study drug;
• Substance abuse or other concurrent medical conditions that, in the Investigator's opinion, could confound study interpretation or affect the patient's ability to tolerate or complete the study.