Sorafenib, Lenalidomide, and Dexamethasone in Treating Patients With Relapsed or Refractory Multiple Myeloma

DISEASE CHARACTERISTICS: * Diagnosis of multiple myeloma * Relapsed or refractory disease requiring treatment * Measurable disease, as defined by at least 1 of the following: * Serum monoclonal protein ≥ 1.0 g * More than 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% (i.e., evaluable disease) * No known standard therapy that is potentially curative for the patient's disease PATIENT CHARACTERISTICS: * ECOG performance status 0-2 * Life expectancy ≥ 12 weeks * ANC ≥ 1,000/μL * Platelet count ≥ 75,000/μL * Hemoglobin ≥ 9 g/dL * Direct bilirubin ≤ 1.5 times upper limit of normal (ULN) * AST ≤ 3 times ULN (≤ 5 times ULN if the liver is involved) * Creatinine ≤ 2.5 times ULN * Patients with treated or untreated POEMS (Patient-Oriented Evidence That Matters) allowed, provided they satisfy the criteria for measurable disease * No other prior malignancy within the past year except currently treated basal cell or squamous cell skin cancer, carcinoma in situ of the cervix or breast, or prostate cancer not requiring therapy * No other active malignancy requiring treatment that would interfere with the assessments of response of the myeloma to protocol treatment * INR \< 1.5 OR PT/PTT ≤ 1.5 times ULN * Patients receiving anticoagulation treatment with an agent such as warfarin or heparin are allowed * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use 2 methods of effective contraception for 28 days prior, during, and for 28 days after discontinuation of lenalidomide * Willing to provide research samples according to the test schedule * No uncontrolled infection * No NYHA classification III or IV heart disease * No unstable angina (i.e., anginal symptoms at rest), new-onset angina (i.e., began within the past 3 months), or myocardial infarction within the past 6 months * No uncontrolled hypertension, defined as systolic blood pressure \> 150 mm Hg or diastolic pressure \> 90 mm Hg, despite optimal medical management * No thrombotic or embolic events within the past 6 months, including cerebrovascular accidents and transient ischemic attacks * More than 4 weeks since prior pulmonary hemorrhage or other bleeding event \> grade 2 * No serious nonhealing wound or ulcer * More than 4 weeks since prior significant traumatic injury * No known positivity for HIV infection or infectious hepatitis, type A, B, or C * No known hypersensitivity to thalidomide or lenalidomide * No prior development of erythema nodosum if characterized by a desquamating rash while taking thalidomide or similar drugs * Able to take aspirin (325 mg) daily as prophylactic anticoagulation PRIOR CONCURRENT THERAPY: * Recovered from prior chemotherapy, regardless of interval since last treatment * Prior lenalidomide therapy allowed * More than 4 weeks since prior experimental therapy * More than 4 weeks since prior major surgery or open biopsy * No concurrent enrollment in any other study involving a pharmacologic agent or investigative therapy (i.e., drug, biologic, immunotherapy approaches, gene therapy) whether for symptom control or therapeutic intent * No other concurrent chemotherapy, immunotherapy, radiotherapy, or any ancillary therapy considered investigational * No concurrent cytochrome P450 enzyme-inducing antiepileptic drugs (i.e., phenytoin, carbamazepine, and phenobarbital), rifampin, or Hypericum perforatum (St. John wort)