Bevacizumab, Lenalidomide, and Dexamethasone in Patients With Relapsed or Refractory Stage II or III Multiple Myeloma

Inclusion Criteria: * Histologically or cytologically confirmed symptomatic multiple myeloma: * Stage II or III disease * Relapsed or refractory disease after \>= 2 courses of prior chemotherapy * Measurable levels of monoclonal protein (M protein) \> 1.0 g/dL by serum protein electrophoresis OR \> 200 mg of monoclonal light chain by 24-hour urine protein electrophoresis * Measurable bone disease, defined as \>= 1 unidimensionally measurable lesion (longest diameter to be recorded) \>= 20 mm with conventional techniques OR \>= 10 mm with spiral CT scan (for patients with lytic bone disease) * No known brain metastases * ECOG performance status (PS) 0-2 OR Karnofsky PS 70-100% * Patients with PS of 3 are eligible if it is due to pain that is likely to improve with treatment * Life expectancy \> 6 months * No known HIV positivity * No abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within the past 6 months * No active infections requiring oral or intravenous antibiotics within the past week * No proteinuria (i.e., albuminuria) \> 1,000 mg/24 hours unless related to the diagnosis of multiple myeloma * Patients with light chain (i.e., "Bence-Jones") proteinuria are still eligible if the non-light chain component of protein is \< 1,000 mg/24 hours * No serious nonhealing wound or ulcer * No blood pressure \> 150/90 mm Hg (even with medication) * No significant traumatic injury within the past 28 days * No clinically significant peripheral vascular disease * No evidence of bleeding diathesis or coagulopathy * No unstable angina or myocardial infarction within the past 6 months * No stroke within the past 6 months * No New York Heart Association class III or IV heart failure * No secondary malignancy within the past 2 years except squamous cell or basal cell carcinoma of the skin or carcinoma in situ of the cervix * Hemoglobin \> 9 g/dL (may be supported by transfusion or growth factors) * WBC \>= 2,000/mm\^3 * Absolute neutrophil count \>= 1,000/mm\^3 * Platelet count \>= 75,000/mm\^3 * Bilirubin =\< 2.5 mg/dL * At least 4 weeks since prior chemotherapy or radiotherapy and recovered * More than 7 days since prior minor surgical procedures, fine-needle aspirations, or core biopsies: More than 24 hours since prior bone marrow biopsy or central veinous access placement * More than 28 days since prior major surgical procedure or open biopsy * At least 4 weeks since prior and no concurrent participation in another experimental drug study * Prior autologous peripheral blood stem cell transplantation allowed * No prior lenalidomide * Concurrent full-dose anticoagulants allowed provided all of the following criteria are met: * No active bleeding or pathological condition that carries a high risk of bleeding (e.g., tumor involving major vessels or known varices) * No thrombocytopenia requiring transfusion * Platelet count \> 75,000/mm3 * INR 2-3 and stable * No concurrent major surgery * No concurrent sargramostim (GM-CSF) * No other concurrent investigational agents * No other concurrent anticancer agents or therapies * AST and ALT =\< 5 times upper limit of normal * Creatinine \< 2.5 mg/dL * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use 2 methods of effective contraception 4 weeks before, during, and 4 weeks after completion of study treatment * No history of allergic reactions attributed to compounds of similar chemical or biological composition to lenalidomide and/or bevacizumab or other agents used in the study