New drug combo aims to prevent transplant complications in blood cancer patients

Copied word for word from the study's registry entry, so the wording is the study team's rather than ours.

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative * Assent, when appropriate, will be obtained per institutional guidelines * Agreement to allow the use of archival tissue from diagnostic tumor biopsies * If unavailable, exceptions may be granted with study principal investigator (PI) approval * Age: =\< 80 years * Note: Patients \> 70 years of age must have Karnofsky performance status \>= 80 and HCT-comorbidity index (CI) =\< 2 * Karnofsky performance status \>= 70% * Patients with the following diagnosis, eligible to undergo allogeneic HCT from an 8/8 match related/unrelated donor (A, B, C, DR by high resolution typing) * Acute leukemias (acute myeloid leukemia \[AML\] or acute lymphoblastic leukemia \[ALL\]) in complete remission with bone marrow (BM) blast of \< 5% * Myelofibrosis (MF): Primary or secondary with high- or intermediate-2 risk per Dynamic International Prognostic Scoring System (DIPSS) * Myelodysplastic syndrome (blast \< 10%) * Myeloproliferative neoplasm (MPN) other than MF needing HCT * Chronic myelomonocytic leukemia (CMML) * Total bilirubin =\< 2 x upper limit of normal (ULN) (unless has Gilbert's disease) (within 30 days prior to day 1 of protocol therapy unless otherwise stated) * Serum glutamic-oxaloacetic transaminase (SGOT) and serum glutamate pyruvate transaminase (SGPT) \< 5 x ULN (within 30 days prior to day 1 of protocol therapy unless otherwise stated) * Creatinine clearance of \>= 60 mL/min per 24 hour urine test or the Cockcroft-Gault formula (within 30 days prior to day 1 of protocol therapy unless otherwise stated) * Left ventricular ejection fraction (LVEF) \>= 50% * Note: To be performed within 30 days prior to day 1 of protocol therapy * If able to perform pulmonary function tests: forced expiratory volume in 1 second (FEV1), forced vital capacity (FVC) and diffusion capacity of the lungs for carbon monoxide (DLCO) (diffusion capacity) \>= 50% of predicted (corrected for hemoglobin) (within 30 days prior to day 1 of protocol therapy) * If unable to perform pulmonary function tests: O2 saturation \> 92% on room air (within 30 days prior to day 1 of protocol therapy) * Seronegative for human immunodeficiency virus (HIV) antigen (Ag)/antibody (Ab) combo, hepatitis C virus (HCV), active hepatitis B virus (HBV) (surface antigen negative), and syphilis rapid plasma reagin (RPR) (within 30 days prior to day 1 of protocol therapy) * If positive, hepatitis C ribonucleic acid (RNA) quantitation must be performed OR * If seropositive for HIV, HCV or HBV, nucleic acid quantitation must be performed. Viral load must be undetectable * Meets other institutional and federal requirements for infectious disease titer requirements * Note: Infectious disease testing to be performed within 28 days prior to day 1 of protocol therapy * Women of childbearing potential (WOCBP): negative urine or serum pregnancy test (within 30 days prior to day 1 of protocol therapy) * If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * 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 at least 6 months after the last dose of protocol therapy * Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only) Exclusion Criteria: * Prior allogeneic HCT * Chemotherapy, radiation therapy, biological therapy, immunotherapy within 21 days prior to day 1 of protocol therapy * Note: Conditioning regimen within 21 days prior to day 1 of protocol therapy is not considered as an exclusion criterion. Patients on maintenance chemotherapy are not excluded * Other investigational drugs for treatment of GVHD * History of allergic reactions attributed to compounds of similar chemical or biologic composition to study agents * Psychological issues, no appropriate caregivers identified, or non-compliant to medication * Clinically significant uncontrolled illness * Uncontrolled infection (bacterial, viral, fungal) * Other active malignancy * Females only: Pregnant or breastfeeding * Any other condition that would, in the investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures * Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)