Inclusion - ANC >= 1500/uL - AST =< 2.5 x ULN - Creatinine =< 1.5 x ULN - Creatinine clearance as calculated by the method of Cockroft and Gault >= 30 mL/minute - Patients with relapsed or refractory multiple myeloma requiring treatment - Patients who have received prior bortezomib therapy will be allowed on trial as long as they did not progress during bortezomib or =< 60 days of therapy discontinuation - Negative serum pregnancy test done =< 7 days prior to registration, for women of childbearing potential (WOCBP) only (a WOCBP is a sexually mature woman who: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months) - Willingness to return to enrolling institution for follow-up - Life expectancy >= 12 weeks - Voluntary written informed consent before performance of any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care - Female subject is either post-menopausal or surgically sterilized or willing to use an acceptable method of birth control (i.e., a hormonal contraceptive, intra-uterine device, diaphragm with spermicide, condom with spermicide, or abstinence) for the duration of the study - Male subject agrees to use an acceptable method for contraception for the duration of the study - Patients have a baseline LVEF >= 45% at baseline - Bisphosphonates are considered to be supportive care rather than therapy, and are thus allowed while on protocol treatment - PLT >= 100,000/uL - Total bilirubin =<1.5 x upper limit of normal (ULN) or if total bilirubin is > 1.5 x ULN, the direct bilirubin must be =< 2.0 mg/dL - Measurable disease of multiple myeloma as defined by at least ONE of the following: - Serum monoclonal protein >= 1.0 g/dL, >= 200 mg of monoclonal protein in the urine on 24 hour electrophoresis, serum immunoglobulin free light chain >= 10 mg/dL AND abnormal serum immunoglobulin kappa to lambda free light chain ratio, monoclonal bone marrow plasmacytosis >= 30% (evaluable disease), or measurable plasmacytoma - ECOG Performance Status (PS) 0, 1, or 2 - Hgb >= 9 g/dl Exclusion - Major surgery, open biopsy (excluding bone marrow) or significant traumatic injury =< 4 weeks prior to registration - Melphalan or other myelosuppressive agents including lenalidomide and non-myelosuppressive agents such as thalidomide or high dose corticosteroids =< 2 weeks prior to registration - Concurrent use of corticosteroids, but patients may be on chronic steroids (maximum dose 20 mg/day prednisone equivalent) if they are being given for disorders other than myeloma, i.e., adrenal insufficiency, rheumatoid arthritis, etc - Uncontrolled infection - Pregnant women or women of reproductive ability who are unwilling to use effective contraception - Nursing women - Men who are unwilling to use a condom (even if they have undergone a prior vasectomy) while having intercourse with any woman, while taking the drug and for 4 weeks after stopping treatment - Other co-morbidity or psychiatric illness which would interfere with patient's ability to participate in this trial - Recent history of myocardial infarction in the six months prior to registration - Uncontrolled angina or electrocardiographic evidence of acute ischemia - Severe uncontrolled ventricular arrhythmias or electrocardiographic evidence of active conduction system abnormalities - Cardiac amyloidosis with hypotension (systolic BP less than 100mmHg) - MGUS or smoldering myeloma - Serious non-healing wound, or ulcer - Known hypersensitivity to Bortezomib, boron or mannitol - Patient has >=Grade 2 peripheral neuropathy within 14 days before enrollment - Patient has received other investigational drugs with 14 days before enrollment - Diagnosed or treated for another malignancy within 2 years of enrollment, with the exception of complete resection of basal cell carcinoma or squamous cell carcinoma of the skin, an in situ malignancy, or low-risk prostate cancer after curative therapy - Infection requiring systemic antibiotic therapy within 14 days preceding the first dose of study drug, or other severe infection - Inability to swallow orally administered medication - Prior allogeneic bone marrow or organ transplantation - Patients who are currently receiving digoxin, cyclosporine, tacrolimus or sirolimus - Severe cardiac comorbidity - Known positive for HIV or active infectious hepatitis, type A, B or C