Bendamustine in Combination With Bortezomib and Pegylated Liposomal Doxorubicin for Multiple Myeloma

Inclusion Criteria: * A histologically established diagnosis of multiple myeloma with evidence of relapse or refractory disease. * Must have a detectable serum or urine M-Protein by protein electrophoresis that is at least 500 mg/dL (serum) or 1 gm/24 hours (urine), respectively, or serum free light chain level \>100 mg/l for the involved free light chain. * Must have received at least one (1) prior line of systemic treatment that has included either lenalidomide or thalidomide. * Must be willing to provide correlative blood samples. Exclusion Criteria: * Must not have received an excessive cumulative dose of anthracycline * No ≥ grade 2 peripheral neuropathy. * No cytotoxic chemotherapy within 30 days prior to registration for protocol therapy. * No autologous stem cell transplant within 6 months prior to registration for protocol therapy * No prior radiation therapy to \> 25% of bone marrow forming bones (i.e., pelvis) within 30 days prior to registration for protocol therapy. See Study Procedures Manual to calculate percent of prior radiation. * No current corticosteroid therapy in doses greater than 10 mg daily of prednisone (or equivalent) if given for management of co-morbid conditions. * No known central nervous system involvement by myeloma. * No poorly controlled intercurrent illness including, but not limited to, ongoing or active infection, poorly controlled diabetes, symptomatic congestive heart failure, cardiac arrhythmia, or psychiatric illness/social climate that in the opinion of the investigator would limit compliance with study requirements. * No patients known to be positive for HIV, or active Hepatitis A, B, or C. * No major surgery within 30 days prior to registration for protocol therapy. Placement of a venous access device within 30 days prior to registration for protocol therapy is allowed.