Donor Stem Cell Transplant in Treating Patients With Relapsed Hematologic Malignancies or Secondary Myelodysplasia Previously Treated With High-Dose Chemotherapy and Autologous Stem Cell Transplant

OBJECTIVES: Primary * To demonstrate the efficacy of performing reduced-intensity conditioning allogeneic hematopoietic cell transplantation in patients with relapsed hematologic malignancies or secondary myelodysplasia after completion of prior high-dose chemotherapy and autologous hematopoietic stem cell transplantation. * To compare the strategy of this regimen with the strategy used in CALGB-100002. Secondary * To describe the response rate at 6 and 12 months in patients treated with this regimen. * To describe the time-to-progression in patients treated with this regimen. * To determine the ability to use pharmacokinetic-directed busulfan to achieve AUC within 20% of target AUC in \> 80% of patients. * To determine percent of donor chimerism in T-cell, myeloid and B-cell populations achieved with this regimen compared with CALGB-100002. * To determine the risk of acute and chronic graft-versus-host disease and other toxicities of this regimen in these patients. * To describe the overall survival and disease-free survival of patients treated on this regimen. * To determine the rate of viral, bacterial, and fungal opportunistic infections occurring in the first year after transplantation compared with CALGB-100002. OUTLINE: This is a multicenter study. * Preparative Regimen: * Busulfan test dose: Patients receive busulfan IV over 45 minutes once during days -14 and -9. * Busulfan treatment dose: Patients receive fludarabine phosphate IV over 30 minutes on days -7 to -3 and busulfan IV over 3 hours on days -6 to -3. * Graft-vs-Host Disease (GVHD) Prophylaxis: * HLA-identical donor: Patients receive antithymocyte globulin IV over 6-10 hours on days -6 to -5; oral tacrolimus twice daily on days -2 to 90 followed by a taper\* as tolerated until day 150 or 180; and methotrexate IV on days 1, 3, and 6. NOTE: \* Tacrolimus may be tapered on days 60-90 if donor chimerism of CD3+ cells is \< 50% at day 60 or patient has progressive disease. * Matched-unrelated donor: Patients receive antithymocyte globulin, tacrolimus, and methotrexate as in HLA-identical donor regimen. Patients also receive oral mycophenolate mofetil twice daily on days 0 to 60. * Allogeneic Stem Cell Transplantation: Patients undergo allogeneic peripheral blood stem cell transplantation on days 0 and 1. Patients then receive filgrastim subcutaneously daily beginning on day 7 and continuing until blood counts recover. * Donor Lymphocyte Infusion (DLI): After day 180 (or day 210 for patients without an HLA-identical donor), patients with stable or progressive disease and no active GVHD may receive up to 3 DLIs every 8 weeks. Blood samples are collected at baseline and then periodically during study therapy for pharmacokinetic studies. After completion of study therapy, patients are followed up every 3 months for 2 years and then every 6 months for up to 5½ years.