Study of Combination Therapy With VELCADE, Doxil, and Dexamethasone (VDd) in Multiple Myeloma

Inclusion Criteria: Each patient must meet all of the following inclusion criteria to be enrolled in the study: * An Institutional Review Board (IRB)-approved signed informed consent * Patient is, in the investigator's opinion, willing and able to comply with the protocol requirements * Age greater than or equal to 18 years * Female patient is either postmenopausal or surgically sterilized or willing to use an acceptable method of birth control (i.e. hormonal contraceptive, intra-uterine device, diaphragm with spermicide, condom with spermicide, or abstinence) for the duration of the study * Male patient agrees to use an acceptable method of contraception for the duration of the study * Expected survival greater than or equal to 3 months * Pre-study Karnofsky performance status \> 60% * Histologic confirmation of multiple myeloma * Patient was previously diagnosed with stage II or III multiple myeloma based on standard criteria and currently requires second or higher line therapy because of progression of disease (PD), defined as a 25% increase in M-protein; development of new or worsening of existing lytic lesions or soft tissue plasmacytomas; or hypercalcemia (\> 11.5 mg/dl); or relapse from complete response (CR) or because of refractory disease, defined as less than minimal response (MR) after 2 cycles of the most recent treatment, including first line of therapy. * Patients with measurable disease defined as: serum monoclonal protein greater than 1 g/dl for IgG type and greater than 0.5 g/dl for IgA type, and, where applicable, greater than 0.2 g/24 hour urine light chain excretion. * Patients with oligosecretory or nonsecretory myeloma will be eligible if measurable disease can be established, such as measurable soft tissue plasmacytoma greater than 2 cm, by either physical examination and/or applicable radiographs (i.e. magnetic resonance imaging \[MRI\], computed tomography \[CT\]-scan) and/or bone marrow involvement greater than 20%. * Patients refractory or relapsing after treatment with any one or two of the agents used in this protocol will be allowed. * Prior radiation therapy will be allowed but radiation therapy must be completed 2 weeks prior to registration. * Left ventricular ejection fraction (LVEF) \> 50% by multiple-gated acquisition (MUGA) or echocardiogram (ECHO) * Patients previously on investigational drugs if no long-term toxicity is expected, and the patients have been off the drugs for one or more weeks * Patient has received less than 250 mg/m2 cumulative dose of doxorubicin or equivalent. * Patient has the following laboratory values at and within 14 days before Baseline (Day 1 of Cycle 1, before study drug administration): * Platelet count \> 50 x 10\^9/L without transfusion support within 7 days before the laboratory test (\> 30 x 10\^9/L if significant bone marrow \[BM\] involvement is present); * Hemoglobin \> 7.5 x 10\^9/L, without transfusion support within 7 days before the laboratory test; * Absolute neutrophil count (ANC) \> 1.0 x 10\^9/L, without the use of colony stimulating factors; * Corrected serum calcium \< 14 mg/dl (3.5 mmol/L); * Aspartate transaminase (AST): \< 2.5 x upper limit of normal (ULN); * Alanine transaminase (ALT): \< 2.5 x ULN; * Alkaline phosphatase: \<1.5 x the ULN; * Total bilirubin: \< 1.5 x the ULN; and * Calculated or measured creatinine clearance: \> 20 mL/minute. Exclusion Criteria: Patients meeting any of the following exclusion criteria are not to be enrolled in the study: * Patient had major surgery within 3 weeks before enrollment. * Patient had a myocardial infarction within 6 months of enrollment or clinical evidence of congestive heart failure. * Patient is known to be human immunodeficiency virus (HIV)-positive (patients assessed to be at risk should be tested). * Patient is known to be hepatitis B surface antigen-positive or has known active hepatitis C infection (patients assessed by the investigator to be at risk should be tested) * Patient has \>= Grade 2 peripheral neuropathy within 14 days before enrollment. * Patient has hypersensitivity to bortezomib, boron or mannitol, or other study drugs. * Serious nonmalignant disease, including uncontrolled diabetes mellitus (DM) or hypertension (HTN), or infection which, in the opinion of the investigator and/or the sponsor, would compromise other protocol objectives