Fludarabine and Total Body Irradiation 800 Centigray (cGy) or 1125 cGy For Allogeneic Stem Cell Transplant Using Graft Versus Host Disease Prophylaxis With Post-Transplant Cyclophosphamide and Tacrolimus, Without Mycophenolate Mofetil

This is a pilot study to evaluate the feasibility, safety and potential benefits of removing one immune suppressive drug called mycophenolate mofetil (MMF) from the standard allogenic stem cell transplant treatment protocol. MMF will be omitted from the transplant regimen in 60 eligible patients with hematologic malignancies. Participants will be followed for up to 2 years post standard of care transplant at Cedars-Sinai.

Inclusion Criteria: * Patient age 18-75 years * Patient has a related donor who is at least Human Leukocyte Antigen (HLA) haploidentical, or an unrelated donor who is a most a single HLA antigen mismatch. * Patient signs the Informed Consent Form for the study * Patient has a hematologic malignancy other than myelofibrosis and meets standard criteria for allogeneic stem cell transplant. * Patient is deemed suitable to receive Fludarabine and Total Body Irradiation (Flu/TBI) 1125 or Flu/TBI 800 conditioning regimen as standard of care transplant * Donor is willing to donate peripheral blood stem cells Exclusion Criteria: * Patient has a diagnosis of myelofibrosis * Patient has high titer antibodies against one or more donor HLA antigens * Patient has undergone prior autologous or allogeneic stem cell transplant. * Inability to collect sufficient peripheral blood stem cells from the donor