Donor T Cells After Donor Stem Cell Transplant in Treating Patients With Hematologic Malignancies

This pilot phase II trial studies how well giving donor T cells after donor stem cell transplant works in treating patients with hematologic malignancies. In a donor stem cell transplant, the donated stem cells may replace the patient’s immune cells and help destroy any remaining cancer cells (graft-versus-tumor effect). Giving an infusion of the donor’s T cells (donor lymphocyte infusion) after the transplant may help increase this effect.