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 ≥ 30% by bone marrow aspirate or biopsy
  • Involved free light chain level ≥ 10 mg/dL

• 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
• 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