CC-4047 and Dexamethasone in Treating Patients With Relapsed or Refractory Multiple Myeloma or Amyloidosis

DISEASE CHARACTERISTICS: * Symptomatic multiple myeloma * Previously treated disease meeting one of the following criteria: * Have light-chain amyloidosis that has been treated with at least one prior regimen * Symptomatic (relapsed or refractory) multiple myeloma * Patients must have received 1-3 treatment regimens * Induction therapy followed by autologous stem cell transplantation and consolidation considered one regimen * Measurable disease, as defined by 1 of the following: * Serum monoclonal protein ≥ 1.0 g by protein electrophoresis * More than 200 mg of monoclonal protein in the urine on 24-hour electrophoresis * Serum immunoglobulin free light chain (FLC) \> 10 mg/dL and an abnormal FLC ratio * Measurable soft tissue plasmacytoma, not previously irradiated * More than 30% plasma cells in bone marrow * At least 10% plasma cells as measured by bone marrow aspirate, bone marrow biopsy, or labeling index * No monoclonal gammopathy of undetermined significance (not applicable for patients with amyloid) * No smoldering myeloma (not applicable for patients with amyloid) PATIENT CHARACTERISTICS: * ECOG performance status 0, 1, or 2 * ANC ≥ 1,000/μL * Platelet count ≥ 75,000/μL * Creatinine ≤ 2.5 mg/dL * Not pregnant or nursing * Women must refrain from breastfeeding during study participation and for at least 28 days after discontinuation of study drug * Negative pregnancy test * Fertile female patients must use two reliable forms of contraception simultaneously at least 28 days before beginning, during, and at least 28 days after completion of study drug * The two methods of reliable contraception must include one highly effective method (i.e., intrauterine device \[IUD\], hormonal \[birth control pills, injections, or implants\], tubal ligation, or partner's vasectomy) and one additional effective (barrier) method (i.e., latex condom, diaphragm, or cervical cap) * Fertile male patients must use a latex condom (even if they have undergone a prior vasectomy) while having intercourse with any woman, while taking the drug and for 28 days after stopping treatment * Men must agree to abstain from donating semen or sperm during study participation and for 28 days after discontinuation of study drug * Willing to abstain from donating blood during study participation and for 28 days after discontinuation of study drug * No uncontrolled infection * No other active malignancy * No New York Heart Association class III or IV cardiac disease (all patients) * Serum troponin T \> 0.10 ng/mL (amyloid patients only) * No known positivity for HIV or active hepatitis infection * No active deep vein thrombosis or pulmonary embolism that has not been therapeutically anticoagulated * No condition, including the presence of laboratory abnormalities, that places the patient at unacceptable risk for participating in the study or confounds the ability to interpret data from the study * No known hypersensitivity to thalidomide or lenalidomide including development of erythema nodosum if characterized by a desquamating rash * No peripheral neuropathy \> grade 2 PRIOR CONCURRENT THERAPY: * All previous cancer therapy, including chemotherapy and investigational agents, must have been discontinued ≥ 2 weeks prior to study registration * No radiotherapy ≤ 14 days prior to study registration * No other concurrent anti-myeloma therapy * No concurrent radiotherapy, except for palliation of a single painful bone lesion or fracture * Routine concurrent bisphosphonate therapy allowed for patients with myeloma bone disease * Willing and able to take aspirin or alternate prophylactic anticoagulation