Adoptive Cellular Immunotherapy Following Autologous Peripheral Blood Stem Cell Transplantation for Multiple Myeloma

Inclusion Criteria: Multiple Myeloma: * Patients must meet criteria for diagnosis of Multiple Myeloma. * Patient must meet either criterion listed below: * Stage I, II, or III newly diagnosed multiple myeloma * Progressive or relapsed disease in partial response (PR) or complete response (CR) * Primary refractory disease. * Relapsed refractory disease. * Patients may have received a prior autologous transplant. * The patients must have recovered from all serious and life threatening effects of previous treatment at the time of study entry (unless this abnormality is believed to be due to the underlying myeloma). * The patient must have adequate bone marrow function, i.e. a total white blood cell count (WBC) of \> 2,000/ul, a Hemoglobin (Hgb) of \> 7 gm/dl, and a platelet count of \> 50,000/ul, unless this abnormality is believed to be due to the underlying myeloma. * The patient must have adequate liver function, i.e. bilirubin \<2.0 mg/dl, aspartate aminotransferase (SGOT), alanine aminotransferase (SGPT) not greater than 2 times the upper normal limit (unless this abnormality is believed to be due to the underlying myeloma). * The patient must have adequate renal function, i.e. serum creatinine \< 3.0 mg/dl, and/or creatinine clearance \>50 ml/min. This eligibility criterion is excluded if renal insufficiency is believed to be secondary to myeloma. * Age \>18 years and \< 75 years old * The patient must have a Karnofsky status \> 80% * Patients must have a life expectancy of at least 12 weeks * Left ventricular ejection fraction of \> 45% by radionuclide scan or echocardiography * Pulmonary function tests: forced vital capacity, Diffusing capacity of the lungs for carbon monoxide (DLCO) and expiratory volume in one second (FEV1) must be \> 50% of predicted * No significant co-morbid medical or psychiatric illness which would significantly compromise the patient's clinical care and chances of survival. * Informed written consent must be obtained. Patients must be able to give informed consent as a prerequisite to this procedure. The Informed Consent form will become part of his/her permanent record and a copy will be given to the patient Exclusion Criteria: * Medical, social, or psychological factors which would prevent the patient from receiving or cooperating with the full course of therapy. * Evidence on physical exam, lumbar puncture, computed tomography (CT), or magnetic resonance imaging (MRI) scan of central nervous system (CNS) involvement with malignancy * Any clinically significant cardiac disease (angina, myocardial infarction, congestive heart failure, ventricular arrhythmias requiring therapy) or clinically significant obstructive/restrictive pulmonary disease * Serology positive for human immunodeficiency virus (HIV) or human T-lymphotropic virus (HTLVI) * Active hepatitis B or C * History of seizures * Concurrent or expected need for therapy with corticosteroids * Active connective tissue disease * Current "clinically significant" pleural effusion, pericardial effusion, or ascites * Positive pregnancy test or presence of lactation * Collection of fewer than 1 x 106 cluster of differentiation 34 positive (CD34+) cells/kg (peripheral blood stem cells). If the apheresis collection is inadequate based on this criteria, the patient will be removed from protocol and a marrow harvest may be performed * A history of a second malignancy (other then squamous cell/ basal cell carcinoma of the skin or cervical dysplasia) must be reviewed by the Principal Investigator, before inclusion or exclusion in the study. Based upon the PI's review, this patient may be eligible (i.e., distant past history of a malignancy)