Bevacizumab With or Without Thalidomide in Treating Patients With Relapsed or Refractory Multiple Myeloma

DISEASE CHARACTERISTICS: * Histologically confirmed progressing multiple myeloma * Stages I, II, or III * More than 25% increase in urine or plasma paraprotein levels * More than 5% malignant plasma cell involvement in bone marrow * Smoldering myeloma is eligible provided there is evidence of progressive disease requiring therapy * At least 25% increase in M protein levels or Bence Jones excretion * Hemoglobin no greater than 10.5 g/dL * Frequent infections * Hypercalcemia * Rise in serum creatinine above normal on 2 separate occasions * Nonsecretory multiple myeloma that is bidimensionally measurable by MRI or CT scan is eligible provided the disease site is new or has shown an increase in M protein levels or Bence Jones excretion is greater than 30% from baseline * No prior or concurrent CNS involvement with primary or metastatic tumor * No nonquantifiable monoclonal proteins or IgM peaks unless there is evidence of bidimensionally measurable disease by MRI or CT scan * No history of hemorrhagic tumor or hemorrhagic metastasis PATIENT CHARACTERISTICS: Age: * 18 and over Performance status: * Karnofsky 70-100% Life expectancy: * At least 3 months Hematopoietic: * See Disease Characteristics * Absolute neutrophil count ≥1,000/mm\^3 * Platelet count ≥ 50,000/mm\^3 * No hemorrhagic illness within the past 3 weeks Hepatic: * Bilirubin ≤ 1.5 mg/dL * SGOT/SGPT≤ 2.5 times upper limit of normal (ULN) * INR ≤ 1.5 * aPTT \< 1.5 times ULN Renal: * See Disease Characteristics * Creatinine ≤ 2 mg/dL * Creatinine clearance ≥ 40 mL/min * Calcium ≤ 12 mg/dL * No nephrotic syndrome Cardiovascular: * No active coronary artery disease * No New York Heart Association class II-IV congestive heart failure * No grade II or greater peripheral vascular disease (i.e, ischemic rest pain, non-healing ulcer, or tissue loss) * No uncontrolled hypertension * No history of deep venous thrombosis * No vascular illness within the past 3 weeks * No arterial thromboembolic event within the past 6 months, including any of the following: * Transient ischemic attack * Cerebrovascular accident * Unstable angina * Myocardial infarction Pulmonary: * No history of pulmonary embolus Other: * No other prior malignancy unless the patient has been in complete remission for at least 2 years * No peripheral neuropathy or CNS abnormalities ≥ grade 2 * Patients with prior exposure to thalidomide and assigned to arm I may have grade 2 peripheral or CNS abnormalities * No seizure disorder * No serious non-healing wound, ulcer, or bone fracture * No trauma within the past 3 weeks * No significant inflammatory illness within the past 3 weeks * No known hypersensitivity to Chinese hamster ovary cell products * No known hypersensitivity to other recombinant human or humanized antibodies and/or positive human antimurine antibodies/human antichimeric antibodies * No other significant medical, psychological, or social problem that would preclude study participation * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception for at least 2 weeks before and during study participation PRIOR CONCURRENT THERAPY: Biologic therapy: * See Chemotherapy * Prior nonmyeloablative transplantation allowed provided the following are true: * Patient is not receiving concurrent immunosuppressive therapy * Patient has no signs of graft-versus-host disease * Concurrent epoetin alfa allowed if started at least 4 weeks prior to study entry Chemotherapy: * No more than 5 prior chemotherapy regimens * Thalidomide, steroids, and interferon are not considered part of prior regimens * Mobilization with chemotherapy followed by either single or tandem autologous transplantation is counted as 1 prior regimen * Mobilization with chemotherapy followed by autologous and subsequent nonmyeloablative HLA-matched sibling allogeneic transplantation is counted as 1 prior regimen * At least 3 weeks since prior chemotherapy * No concurrent chemotherapy Endocrine therapy: * See Chemotherapy * At least 2 weeks since prior steroids * No concurrent steroids Radiotherapy: * At least 3 weeks since prior radiotherapy * No concurrent radiotherapy Surgery: * At least 3 weeks since prior surgery, including biopsy of a visceral organ Other: * At least 10 days since prior anticoagulants, including aspirin * At least 2 days since prior nonsteroidal anti-inflammatory agents * Concurrent bisphosphonates allowed