Cytokine-Treated Veto Cells in Treating Patients With Hematologic Malignancies Following Stem Cell Transplant

Patient Inclusion Criteria: * Age 12-75 years. The first 3 subjects will be 18 years of age to gain experience and observe safety. After 3 adult subjects have successfully engrafted and if the safety profile is tolerable, adolescents age 12 may be enrolled on to the trial * Patients with a diagnosis either follicular lymphoma (FL), mantle cell lymphoma (MCL), chronic lymphocytic leukemia (CLL), multiple myeloma (MM), Hodgkin's lymphoma (HL), non-Hodgkin's lymphoma (NHL), chronic myeloid leukemia (CML), myelodysplastic syndrome, myeloproliferative syndromes (MPD), acute myeloid leukemia (AML) or acute lymphoid leukemia (ALL). * Patients with aplastic anemia and severe immune deficiency or nonmalignant bone marrow failure states. Patients with severe thalassemia requiring regular blood transfusions or sickle cell disease with severe clinical features (these include any clinically significant sickle genotype, for example, hemoglobin SS (Hb SS), hemoglobin SC (Hb SC), hemoglobin S beta thalassemia (Hb Sbeta), or Hemoglobin S-OArab genotype\] with at least one of the following manifestations: * Clinically significant neurologic event (stroke) or neurological deficit lasting \> 24 hours; * History of two or more episodes of acute chest syndrome (ACS) in the 2-year period preceding enrollment or referral despite adequate supportive care measures (i.e. asthma therapy); * An average of three or more pain crises per year in the 2-year period preceding enrollment or referral (re…