Inclusion Criteria:

• Subject must voluntarily sign and understand written informed consent.
• Confirmed diagnosis of multiple myeloma as specified by the SWOG criteria and is detailed in Appendix I.

• Measurable disease as defined the following:

  1. For patients post induction therapy, any measurable paraprotein in the serum or urine and/or any plasmacytoma present on physical exam or imaging.
  2. For patients with relapsed/refractory disease, > 0.5 g/dL serum monoclonal protein, > 0.1 g/dL serum free light chains, > 0.2 g/24 hrs urinary M-protein excretion, and/or measurable plasmacytoma(s).
• Age > or = than 18 years at the time of signing the informed consent form.
• Karnofsky performance status> or =70% (>60% if due to bony involvement of myeloma).
• Group A (post-induction therapy)- patients who have received only one prior treatment regimen (eg VAD, Thal/Dex, BLT-D, MP, BiRD, or DVd) with at least 20 patients having received a Revlimid based regimen or Group B(>1st line of therapy)- patients with relapsed/refractory multiple myeloma who have received two or more prior treatment regimens .
• If the patient is a woman of childbearing age, she must have a negative serum or urine pregnancy test within 7 days of starting study and must use effective contraception throughout the course of the study.
• Life expectancy > 12 weeks.
• Absolute neutrophil count (ANC)> or = 1500 cells/mm3 (> or = 1000 for patients with bone marrow biopsy displaying > 50% involvement by myeloma)
• Platelets count > or = 50,000/mm3 (> or = 30,000 for patients with bone marrow biopsy displaying > 50% involvement by myeloma)
• Hemoglobin > 9.0 g/dL
• Serum SGOT/AST <3.0 x upper limits of normal (ULN)
• Serum SGPT/ALT <3.0 x upper limits of normal (ULN)
• Serum creatinine < 2.5 mg/dL or creatinine clearance > 40ml/min
• Serum total bilirubin < 1.5 x ULN
• Patients must have a MUGA scan with LVEF >50%

Exclusion Criteria:

• Patients with non-secretory MM (no measurable monoclonal protein, free light chains, and/or M-spike in blood or urine) unless measurable disease is available with imaging techniques such as MRI and PET scan.
• Prior treatment with bortezomib.
• Peripheral neuropathy of > Grade 2 as defined by CTCAE Version 3.0 (see Appendix II)
• History of allergic reactions to compounds containing mannitol, bortezomib, conventional formulation of doxorubicin HCL or the components of DOXIL.
• Prior history of other malignancies (except for basal cell or squamous cell carcinoma of the skin or carcinoma in situ of the cervix or breast) unless disease free for ³ 5 years.
• NYHA Class III or IV heart disease. History of active unstable angina, congestive heart disease, serious uncontrolled cardiac arrhythmia or myocardial infarction within 6 months.
• Female patients who are pregnant or breastfeeding. Women of childbearing potential and men must agree to use adequate contraception prior to study entry and for the duration of study participation.
• Known HIV or hepatitis A, B, or C positivity
• Active viral or bacterial infections or any coexisting medical problem that would significantly increase the risks of this treatment program.
• Any concurrent, uncontrolled medical condition, laboratory abnormality, or psychiatric illness which could place him/her at unacceptable risk, including, but not limited to, uncontrolled hypertension, uncontrolled diabetes, active uncontrolled infection, and/or acute chronic liver disease (i.e., hepatitis, cirrhosis).
• No prior anti-myeloma therapy within 2 weeks of treatment initiation.