BB-10901 in Treating Patients With Relapsed and/or Refractory Multiple Myeloma

DISEASE CHARACTERISTICS: * Histologically confirmed multiple myeloma * Relapsed or relapsed/refractory disease * Failed ≥ 1 prior therapy for multiple myeloma * Once the MTD is defined, only patients who have received at least 1 but equal or less than 6 prior chemotherapy regimens will be enrolled at this dose level * CD56-positive disease confirmed by immunohistochemistry or flow cytometry PATIENT CHARACTERISTICS: * ECOG (Zubrod) performance status 0-2 * Life expectancy ≥ 12 weeks * Platelet count ≥ 75,000/mm\^3 * Absolute neutrophil count \> 1,000/mm\^3 * Hemoglobin ≥ 8.5 g/dL * AST and ALT ≤ 3 times upper limit of normal (ULN) * Bilirubin ≤ 1.5 times ULN * Amylase and lipase within normal limits * Creatinine ≤ 2 mg/dL * Left ventricular ejection fraction ≥ lower limit of normal on MUGA or ECHO * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * No peripheral neuropathy ≥ grade 3 or painful grade 2 neuropathy * No significant cardiac disease, including any of the following: * Myocardial infarction within the past 6 months * Unstable angina * Uncontrolled congestive heart failure * Uncontrolled hypertension (i.e., recurrent or persistent increases in systolic blood pressure ≥ 180 mm Hg or diastolic blood pressure ≥ 110 mm Hg) * Uncontrolled cardiac arrhythmias * Cardiac toxicity ≥ grade 3 after prior chemotherapy * No history of multiple sclerosis or other demyelinating disease * No hemorrhagic or ischemic stroke within the past 6 months * No Eaton-Lambert syndrome (para-neoplastic syndrome) * No CNS injury with residual neurological deficit (other than peripheral neuropathy ≤ grade 2) * No other malignancy within the past 3 years except adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer, in situ breast cancer, or in situ prostate cancer * No clinically relevant active infection, including active hepatitis B or C infection or HIV infection * No other condition or disease, including laboratory abnormalities, that, in the opinion of the investigator, may preclude study treatment * No known recent biochemical or clinical evidence of pancreatitis or extensive metastatic disease involving the pancreas PRIOR CONCURRENT THERAPY: * See Disease Characteristics * At least 4 weeks since prior chemotherapy (6 weeks for nitrosoureas or mitomycin C) * At least 4 weeks since prior radiotherapy * At least 4 weeks since prior major surgery (except placement of a vascular access device or tumor biopsies) * More than 4 weeks since prior investigational agents * At least 2 weeks since prior antineoplastic therapy with biological agents * No prior hypersensitivity to monoclonal antibody therapy * No other concurrent investigational agents * No concurrent corticosteroids (except as indicated for other medical conditions \[\< 10 mg prednisone or equivalent\]; as pre-medication for administration of certain medications or blood products \[≤ 100 mg hydrocortisone\]; or for treatment of infusion reactions) * Concurrent topical steroids allowed * No other concurrent antineoplastic treatment (e.g., chemotherapy, radiotherapy, or biological agents) * Concurrent bisphosphonates allowed provided patient began bisphosphonates before study entry and is maintained on a stable dose during study treatment