T Cell Immunotherapy for Multiple Myeloma Patients Undergoing a Bone Marrow Transplant

Patient Inclusion Criteria * Previous diagnosis of multiple myeloma based on standard criteria. Tests need not be performed within 30 days of registration. * Durie-Salmon Stage II or III disease at any time since diagnosis * Induction therapy with a minimum of 3 cycles of chemotherapy or 3 months of high-dose corticosteroids without progressive disease. (Note: no glucocorticoids are allowed within 3 weeks of registration; see exclusion criteria.) * Measurable serum and/or urine M-protein from prior to induction therapy documented and available * Lymphocyte subsets by flow cytometry demonstrating CD3+ \>= 10% of the peripheral white blood cell count, and CD4+/CD8+ \>= 0.30. Test must be obtained following completion of induction therapy. * Meets all institutional criteria for and has institutional approval to undergo autologous peripheral blood stem cell transplantation * Age \>= 18 years old and \<=70 years old * ECOG performance status of 0 or 1 * Life expectancy \> 6 months * Females of child-bearing potential must have a negative serum bHCG test and be willing to use effective contraception (i.e. a hormonal contraceptive, intra-uterine device, diaphragm with spermicide, or condom with spermicide, or abstinence) up to Day 180. * Negative test results for current/active infection with HIV-1, HIV-2, hepatitis B, and hepatitis C within 60 days of registration.(Antibody, antigen and nucleic acid tests acceptable, depending on institutional standards.) * Corrected serum calcium \< 11 mg/dL, and no evidence of symptomatic hypercalcemia. (Corrected serum calcium is calculated by adding 0.8 mg/dL to the measured serum calcium for every 1 g/dL that the serum albumin falls below 4.0 g/dL.) * Serum total bilirubin and SGPT (ALT) \< 2.0 times the upper limit of normal * Serum creatinine \< 2.0 mg/dL * No detectable human anti-mouse antibody (HAMA) titer, and no history of allergies to mice or murine (mouse) proteins * The patient must be able to comprehend and have signed the informed consent Patient Exclusion Criteria * Diagnosis of any of the following cancers: * POEMS syndrome (plasma cell dyscrasia with polyneuropathy, organomegaly, endocrinopathy, monoclonal protein \[M-protein\] and skin changes) * Non-secretory myeloma * Plasma cell leukemia * Diagnosis of amyloidosis * Progression or relapse presently or in the past, during or following therapy for multiple myeloma * Previous hematopoietic stem cell transplantation * Use of corticosteroids (glucocorticoids) within 21 days of registration * Infection requiring treatment with antibiotics, antifungal, or antiviral agents within seven days of registration * Participation in any clinical trial, within four weeks prior to registration on this trial, which involved an investigational drug or device * History of malignancy other than multiple myeloma within five years of registration, except adequately treated basal or squamous cell skin cancer. Any other exceptions must be discussed with Xcyte Therapies' Medical Monitor prior to registration. * History of an autoimmune disease (e.g., rheumatoid arthritis, multiple sclerosis, systemic lupus erythematosis) requiring systemic treatment. Hypothyroidism without evidence of Grave's Disease or Hashimoto's thyroiditis is permitted. * Evidence of spinal cord compression * Major organ system dysfunction including (but not limited to): New York Heart Association Class III or IV, pulmonary disease requiring the use of inhaled steroids or bronchodilators, renal, hepatic, gastrointestinal, neurologic, or psychiatric dysfunction which would impair patient's ability to participate in the trial