Donor Peripheral Stem Cell Transplant in Treating Patients With Hematolymphoid Malignancies

PRIMARY OBJECTIVES: I. To determine the feasibility of purifying allogeneic CD8+ memory T-cells suitable for clinical application and to determine the safety and maximum tolerated dose (MTD) of these cells in patients with recurrent or refractory hematolymphoid malignancies following allogeneic hematopoietic cell transplant (HCT). SECONDARY OBJECTIVES: I. To determine disease response, time to disease progression, event-free survival, and overall survival following treatment with allogeneic CD8+ memory T-cells. II. To assess donor specific chimerism before and at designated time points after treatment with allogeneic CD8+ memory T-cells. OUTLINE: This is a dose-escalation study. Patients undergo CD8+ memory T-cell infusion over 10 to 20 minutes.