Aflibercept for Relapsed Multiple Myeloma

Inclusion Criteria: * Histologically or cytologically confirmed multiple myeloma * Stage II or III disease according to Salmon-Durie staging criteria * Relapsed or refractory disease * Progressive disease * Measurable disease, defined by ≥ 1 of the following criteria: * Serum M protein ≥ 1.0 g/dL by serum protein electrophoresis * Free light chain measurement \> 200 mg/dL * Urinary M protein excretion ≥ 200 mg/24 hours * Must have received ≥ 2 prior therapies\* for multiple myeloma that meet the following criteria: * Antimyeloma therapeutic regimen consisting of ≥ 1 complete course of single-agent or combination-agent therapy, or a planned series of treatments (e.g., 3-4 courses of induction therapy followed by a stem cell harvest procedure followed by conditioning high-dose therapy supported by stem cell transplantation) * Antimyeloma regimen is discontinued because of the development of resistant disease or severe therapy-related toxicity * Individual antimyeloma regimen will be considered to have been discontinued when all agents of the regimen have been permanently stopped * A prior regimen will not be considered to have been discontinued for the modification of drug doses, or if less than all the agents of a combination regimen have been discontinued, or if the regimen has been halted temporarily for the development of a plateau phase of myeloma * Maintenance therapy will not be considered an additional regimen * If new agents are added to an existing regimen, presumably because of tumor resistance, the old regimen will be considered to have ended and a new regimen to have started * No evidence of central nervous system (CNS) disease, including primary brain tumor or brain metastasis * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0-2 OR Karnofsky PS 60-100% * Life expectancy \> 12 weeks * White blood cell (WBC) ≥ 3,000/mm\^3 * Absolute neutrophil count ≥ 1,500/mm\^3 * Platelet count ≥ 75,000/mm\^3 * Bilirubin ≤ 1.5 times upper limit of normal (ULN) * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 2.5 times ULN * Creatinine ≤ 2.0 mg/dL OR creatinine clearance ≥ 60 mL/min * No albuminuria only * Urine protein: creatinine ratio \< 1 OR 24-hour urine protein with an albumin level \< 500 mg * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception during and for ≥ 6 months after completion of study therapy Exclusion criteria: * No known hypersensitivity to Chinese hamster ovary cell products or other recombinant human antibodies * No known history of allergic reactions attributed to compounds of similar chemical or biological composition to other agents used in the study * No serious or nonhealing wound, ulcer, or bone fracture * No significant traumatic injury within the past 28 days * No abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within the past 28 days * No clinically significant cardiovascular disease * No prothrombin time (PT) or international normalized ratio (INR) \> 1.5 (unless patient is on full-dose warfarin) * No evidence of bleeding diathesis or coagulopathy * No uncontrolled intercurrent illness that would limit compliance with study requirements, including ongoing or active infection * No psychiatric illness or social situations that would limit study compliance * No concurrent major surgery * No concurrent immunosuppressive agents (including steroids) * No other concurrent investigational agents