Fludarabine Phosphate, Cyclophosphamide, Total Body Irradiation, and Donor Stem Cell Transplant in Treating Patients With Blood Cancer

PRIMARY OBJECTIVES: I. To evaluate the rate of relapse, defined as recurrence of underlying disease or progression of underlying disease, at 1 year in patients who receive haploidentical peripheral blood stem cells (PBSCs) after reduced intensity conditioning and post-transplant cyclophosphamide and tocilizumab (or tocilizumab alternative). SECONDARY OBJECTIVES: I. To evaluate safety including development of acute graft versus host disease (GVHD) and death at 100 days post-transplant, as well as other treatment related toxicities including chronic GVHD, engraftment rate, non-relapse mortality, progression free survival (PFS) at one year, and overall survival (OS) at one year, as compared with historical controls. TERTIARY OBJECTIVES: I. Correlative studies will include chimerism analysis by molecular analysis and evaluation of immune reconstitution by cytomegalovirus (CMV) dextramer analysis using flow cytometry. OUTLINE: Patients receive fludarabine phosphate intravenously (IV) over 30 minutes on days -6 to -2 and cyclophosphamide IV over 2 hours on days -6 and -5. Patients undergo total body irradiation (TBI) on days -1 and peripheral blood stem cell transplantation (PBSCT) on day 0. After completion of study treatment, patients are followed up at 30 and 100 days.