Study of Vorinostat With Doxil and Bortezomib for Patients With Relapsed/Refractory Multiple Myeloma

Inclusion Criteria: Relapsed or relapsed and refractory multiple myeloma: * Relapsed MM is defined as clinically active disease, in patients who have received one or more prior therapies, that is not refractory to the most recent treatment. (Refractory to the prior treatment means either progressive disease (PD) on last prior therapy; best response of stable disease (SD) to last prior therapy, or PD within 60 days of completing therapy). * Relapsed and refractory MM is defined as relapsed disease, which either becomes non-responsive while on salvage therapy, or progresses within 60 days of last therapy. 1 to 3 prior lines of therapy for multiple myeloma (a single line of treatment may consist of 1 or more agents and regimens. A single line of therapy may be most easily delineated by a response to treatment followed by a change in treatment due to the progression of disease. * Prior bortezomib- and anthracycline-based therapy is allowed; prior cumulative doxorubicin dose must be \<360 mg/m2 (or its equivalent) * Prior autologous stem cell transplantation is allowed provided the patient is 3 months out from transplant and has recovered from any transplant-related toxicities (to baseline or grade 1 in severity) All prior treatment-related non-hematologic toxicities resolved to ≤Grade 1 (or baseline), not including alopecia Prior radiation therapy completed ≥2 weeks prior to day 1 of treatment Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 Age ≥18 years Life expectancy of at least 6 months Adequate bone marrow function (without platelet or RBC transfusion support within one week of screening) as demonstrated by: * Hemoglobin ≥ 8 g/dL (use of erythropoietin stimulating agent is OK) * Absolute neutrophil count (ANC) ≥ 1,000 cells/mm3 (without granulocyte growth factor support) * Platelet count ≥ 100,000/mm3 (≥75,000/mm3 in patients with ≥30% marrow involvement of MM who are felt to have thrombocytopenia primarily due to marrow infiltration of disease as opposed to diminished marrow reserves from prior therapy) Adequate hepatic and renal function as demonstrated by: * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 2.5 x upper limit of normal (ULN) * Total serum bilirubin ≤1.5 x ULN * Creatinine clearance (CrCL) ≥ 30mL/min as measured via Cockcroft-Gault or 24-hour urine testing Documented negative serologic testing for hepatitis B (HBV) and Hepatitis C (HCV) as measured by the following (NOTE: this testing is not necessary if patient has had negative testing within the last year, and no subsequent risk factors for acquisition of these viruses): * HBV surface antigen, surface antibody, and core antibody (NOTE: patients who are seropositive because of hepatitis B vaccine are eligible) * HCV antibody. * For patients with serologic evidence of viral hepatitis, quantitative PCR will be performed. Documented negative HIV blood test (NOTE: this testing is not necessary if patient has had negative testing within the last year, and no subsequent risk factors for acquisition of this virus) Adequate cardiac function, defined as: * No EKG evidence of acute ischemia * No EKG evidence of active clinically significant conduction system abnormalities * No EKG evidence of \> Grade 2 (\>480 ms) QTc prolongation * Prior to study entry, any ECG abnormality at screening not felt to put the patient at risk has to be documented by the investigator as not medically significant * No uncontrolled angina or severe ventricular arrhythmias * No clinically significant pericardial disease * No history of myocardial infarction within the last 6 months * Left ventricular ejection fraction (LVEF) must be \> 45% by either echocardiography or radionuclide-based multiple gated acquisition (MUGA) * No Class II or higher New York Heart Association Congestive Heart Failure Negative serum β-hCG pregnancy test within 72 hours of day 1 of treatment with study medications in women of child-bearing potential All males and females of childbearing potential must agree to use an effective contraceptive method during the study and for 3 months following the last dose of study treatment. Effective contraception is defined as any medically recommended method (or combination of methods) as per standard of care, including abstinence. Females of non-childbearing potential are those who are postmenopausal greater than 1 year or who have had a bilateral tubal ligation or hysterectomy Exclusion Criteria: * \> 3 prior lines of therapy for treatment of MM Receipt of prior allogeneic stem cell/bone marrow transplantation Primary refractory MM as defined by the ASH/FDA Workshop on Clinical Endpoints in Multiple Myeloma\[24\] Peripheral neuropathy (PN) ≥ grade 1 with pain or ≥grade 2 PN within 14 days prior to enrollment Known history of HIV, HBV or HCV infection Serum potassium ≤3.0 mmol/L or serum magnesium ≤1.6mg/dL that cannot be corrected with supplementation Known hypersensitivity to bortezomib or any of its components (boron, mannitol), vorinostat, doxorubicin, or any of the components of PLD; Patients with a history of reactions to other liposomal drug formulations will be evaluated individually, and if their reactions were felt to have been due to the liposome itself, as opposed to the encapsulated agent, they will be excluded at the discretion of the investigators. Prior or concomitant use of a histone deacetylase inhibitor (exception: prior valproic acid for epilepsy is allowed provided patient undergoes a 30 day wash out prior to D1 of study treatment) No major surgery within 3 weeks prior to day 1 of study treatment Active, serious infection, medical, or psychiatric condition that would represent an inappropriate risk to the patient or would likely compromise achievement of the primary study objective Other prior or concomitant malignancies with the exception of: * Non-melanoma skin cancer * In-situ malignancy * Low-risk prostate cancer after curative therapy * Other cancer for which the patient has been disease free for ≥ 3 years Pregnant or lactating women