RATIONALE: Sorafenib may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth and by blocking blood flow to the cancer.

PURPOSE: This phase II trial is studying how well sorafenib works in treating patients with relapsed or refractory multiple myeloma.

OBJECTIVES:

• Determine the overall response rate (confirmed complete response, response, and partial response) in patients with relapsed or refractory multiple myeloma treated with sorafenib.
• Determine the qualitative and quantitative toxic effects of this drug in these patients.
• Determine the overall and progression-free survival of patients treated with this drug.
• Correlate gene expression signatures with response in patients treated with this drug.

OUTLINE: This is a multicenter study.

Patients receive oral sorafenib twice daily on days 1-28. Courses repeat every 28 days in the absence of disease progression or unacceptable toxicity.

After completion of study treatment, patients are followed periodically for 3 years.

PROJECTED ACCRUAL: A total of 40 patients will be accrued for this study.

DISEASE CHARACTERISTICS:

• Diagnosis of active multiple myeloma
• Previously treated disease
• Measurable disease, as defined by ≥ 1 of the following criteria:
• Serum M-protein level ≥ 1 gm/dL by serum protein electrophoresis
• Urinary M-protein excretion ≥ 0.2 g/24 hours by urine electrophoresis
• Bone marrow plasmacytosis 20% by bone marrow aspirate
• Monoclonal serum free light chains > 5 times normal plus abnormal kappa:lambda ratio by Freelite test
• Relapsed or refractory disease, as defined by 1 of the following criteria:
• Relapsed disease after prior autologous stem cell transplantation
• Relapsed or refractory disease after ≥ 1 prior therapy for myeloma
• No evidence of POEMS (polyneuropathy, organomegaly, endocrinopathy, presence of M-protein, and skin changes) syndrome

PATIENT CHARACTERISTICS:

Performance status

• Zubrod 0-2

Life expectancy

• Not specified

Hematopoietic

• Absolute neutrophil count > 750/mm^3
• Platelet count > 75,000/mm^3
• No evidence of bleeding diathesis

Hepatic

• Bilirubin ≤ 1.5 times upper limit of normal (ULN)
• AST or ALT ≤ 5 times ULN

Renal

• Creatinine normal

Cardiovascular

• No significant history of cardiac disease
• No myocardial infarction within the past 6 months
• No congestive heart failure
• No unstable angina pectoris
• No cardiac ventricular arrhythmia requiring medication
• No uncontrolled hypertension

Other

• Not pregnant or nursing
• Negative pregnancy test
• Fertile patients must use effective contraception
• Must be able to take oral medications without crushing, dissolving, or chewing tablets
• No significant neurotoxicity ≥ grade 2
• No active infection requiring antibiotics
• No uncontrolled diabetes
• No serious medical or psychiatric illness that would preclude study participation
• No other prior malignancy within the past 3 years except adequately treated basal cell or squamous cell skin cancer or carcinoma in situ of the cervix

PRIOR CONCURRENT THERAPY:

Biologic therapy

• See Disease Characteristics
• More than 6 weeks since prior autologous stem cell transplantation

Chemotherapy

• At least 3 weeks since prior myelosuppressive chemotherapy (6 weeks for nitrosoureas)
• At least 2 weeks since prior nonmyelosuppressive chemotherapy

Radiotherapy

• At least 2 weeks since prior external-beam radiotherapy

Other

• Recovered from all prior treatment
• No prior sorafenib
• No concurrent cytochrome P450 enzyme-inducing antiepileptic drugs (e.g., phenytoin, carbamazepine, or phenobarbital)
• No concurrent rifampin or Hypericum perforatum (St. John''''s wort)
• No concurrent therapeutic anticoagulation