Sorafenib and Bortezomib Treatment for Relapsed or Refractory Multiple Myeloma Patients

Inclusion Criteria: * Eligible participants must have been previously diagnosed using standard criteria and have received no more than 2 prior regimens for the treatment of multiple myeloma. * Participant must be defined as Relapsed or Refractory Disease by one of the following criteria prior to enrollment: Relapsed Disease after high-dose therapy (autologous stem cell transplantation) as part of the first-line line treatment program. These patients may have received a maximum of 1 previous regimen, Refractory Disease or Relapsed Disease after \> 1 prior therapy for multiple myeloma. Prior bortezomib treatment permitted if the patient achieved a documented response. * ECOG performance status 0, 1, or 2. * WBC \>= 3000; ANC \>= 1000; platelets \>= 50,000 (Patients with platelets \>= 30,000 are eligible if thrombocytopenia is felt to be due to extensive bone marrow involvement with myeloma). * Serum creatinine \< 2.0 mg/dL for a calculated or measured creatinine clearance \> 30 mL/minute * Total bilirubin \< 1.5 x ULN * ALT and AST \< 2.5 x the ULN ( \< 5 x ULN for patients with liver involvement) * INR \< 1.5 or a PT/PTT within normal limits. Patients receiving anti-coagulation treatment with an agent such as warfarin or heparin may be allowed to participate. For patients on warfarin, the INR should be measured prior to initiation of sorafenib and monitored at least weekly, or as defined by the local standard of care, until INR is stable. * Patients must have measurable or evaluable disease. In patients with disease limited to bone and bone marrow, serial paraprotein measurements are acceptable for evaluable disease. Exclusion Criteria: * Patients with \> grade 1 peripheral neuropathy. * Thrombolic or embolic events such as a cerebrovascular accident, including transient ischemic attacks, within the past 6 months. * Pulmonary hemorrhage/bleeding event \> CTCAE Grade 2 within 4 weeks of first dose of study drug. * Any other hemorrhage/bleeding event \> CTCAE Grade 3 within 4 weeks of first dose of study drug. * Known brain metastasis. Patients with neurological symptoms must undergo CT scan/MRI of the brain to exclude brain metastasis. * Patients with other medical conditions that would potentially interfere with their participation in this trial. * Patients with other active malignancies, or history of treatment for other invasive cancers, within 3 years of study entry. * Patients with previous evidence of hypersensitivity to sorafenib, bortezomib, boron, or mannitol. * Women who are pregnant or lactating are ineligible. All patients of childbearing potential are required to use adequate methods of contraception while receiving study treatment, and for at least 2 weeks after the last dose of sorafenib. Men should continue to use contraception until at least 3 months after their last dose of sorafenib. * Evidence of POEMS (polyneuropathy, organomegaly, endocrinopathy, monoclonal gammopathy, and skin changes) syndrome. * Cardiac disease: Congestive heart failure \> class II NYHA (see Appendix D.) Patients must not have unstable angina (anginal symptoms at rest), new onset angina (began within the last 3 months), or myocardial infarction within the past 6 months. * Cardiac ventricular arrhythmias requiring anti-arrhythmic therapy. * Uncontrolled hypertension defined as systolic blood pressure \> 150 mmHg or diastolic pressure \> 90 mmHg, despite optimal medical management. * Known human immunodeficiency virus (HIV) infection or chronic Hepatitis B or C. * Active clinically serious infection \> CTCAE Grade 2.