Intentional Rejection of the Donor Graft Using Recipient Leukocyte Infusion(s) Following Nonmyeloablative Allogeneic Stem Cell Transplant

Inclusion Criteria: 1. Patients with chemorefractory non-Hodgkin's or Hodgkin's lymphoma or multiple myeloma. Criteria for consideration of enrollment will include: 1. primary refractory or refractory relapsed disease for which autologous HCT is unlikely to be beneficial; 2. relapse after autologous HCT 3. ineligibility for standard myeloablative or nonmyeloablative allo-HCT because of either lack of a donor or patient considerations 2. Non Hodgkin's lymphoma, or Hodgkin's lymphoma: primary refractory or refractory relapse 3. Multiple myeloma; primary refractory or refractory relapse 4. Patients with the above malignancies who have had a previous autologous or allogeneic bone marrow or stem cell transplant. 5. An estimated disease-free survival of less than one year. 6. Age 18 to age \< 75 years 7. ECOG performance status of 0, 1, or 2. Exclusion Criteria: 1. Patients whose life expectancy is limited by diseases other than their malignancy 2. Patients who have a 5/6 or better matched related donor or a 4/6 or better umbilical cord blood donor and who are medically eligible for conventional myeloablative or non-myeloablative transplant will be excluded 3. Cardiac disease: symptomatic congestive heart failure or RVG or echocardiogram determined LVEF ogf\< 30%, active angina pectoris or uncontrolled hypertension 4. Pulmonary disease: severe chronic obstructive lung disease, or symptomatic restrictive lung disease, or corrected DLCO \< 40% of predicted 5. Renal disease: serum creatinine \> 3.0 mg/dl. 6. Hepatic disease: serum bilirubin \> 3.0 mg/dl or alkaline phosphatase, SGOT or SGPT \> 3 x ULN 7. Neurologic disease: symptomatic leukoencephalopathy, active CNS malignancy or other neuropsychiatric abnormalities believed to preclude transplantation (pervious CNS malignancy presently in CR is not an exclusion) 8. Uncontrolled infection. 9. Recipient leukocyte infusion (RLI) might involve the infusion of circulating tumor cells to the patients. To minimize this risk patients who have evidence of circulating tumor cells by light microscopy and flow cytometry will be excluded 10. Patients with acute leukemia will be excluded because they will likely have much greater circulating tumor burden, which would increase the risk of infusion of clonal tumor cells