Human Lysozyme Goat Milk for the Prevention of Graft Versus Host Disease in Patients With Blood Cancer Undergoing a Donor Stem Cell Transplant

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative * Willingness to be followed for the planned duration of the trial (2 years) * All subjects must have the ability to understand and the willingness to sign a written informed consent * Karnofsky performance status \>= 60 per COH SOP * Patients must be undergoing allogeneic hematopoietic stem cell transplantation (alloHCT) for hematologic malignancies from matched related or matched unrelated donors with 8/8 (A, B, C, DRB 1) high resolution human leukocyte antigen (HLA) donor allele matching * Patients must be receiving a fractionated total body radiation (FTBI) based- myeloablative conditioning regimen; (acceptable conditioning regimens include total body irradiation \[TBI\] + cyclophosphamide or TBI + etoposide) * Ejection fraction measured by echocardiogram or multi gated acquisition scan (MUGA) \> 50% * Diffusing capacity for carbon monoxide (DLCO) adjusted for hemoglobin or forced vital capacity (FVC) \> 50% predicted * Total serum bilirubin \< 2 times upper limit of normal * Alanine aminotransferase (ALT)/aspartate aminotransferase (AST) =\< 2.5 x the upper normal limit * Alkaline phosphatase =\< 2.5 x the upper normal limit * Measured creatinine clearance more than 60 mL/min * Agreement by females and males of childbearing potential to use an effective method of birth control or abstain from heterosexual activity for the course of the study through 90 days afte…