Itacitinib, Tacrolimus, and Sirolimus for the Prevention of GVHD in Patients With Acute Leukemia, Myelodysplastic Syndrome, or Myelofibrosis Undergoing Reduced Intensity Conditioning Donor Stem Cell Transplantation

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

Performance status: Karnofsky \>= 70%

Patients with neoplastic hematologic disorders with indication of allogeneic transplant according to the standard guidelines as follows:

* Acute leukemia (AL) in first complete response (CR1) or subsequent complete response (CR) or active disease with bone marrow (BM) blast of \< 5%

* Myelodysplastic syndrome (MDS) with intermediate-2 or high risk per International Prognostic Scoring System (IPSS) or

* Myelofibrosis; primary or secondary if intermediate-2 or high risk per Dynamic International Prognostic Scoring System (DIPPS)

All candidates for this study must have a matched related donor (MRD) who is willing to donate BM or peripheral blood stem cells or an 8/8 allele matched unrelated donor (MUD)

Total bilirubin =\< 1.5 X upper limit of normal (ULN) (unless has Gilbert's disease) (performed within 28 days prior to day 1 of protocol therapy unless otherwise stated. In case of active disease, evaluation should be done within 15 days)

Aspartate aminotransferase (AST) =\< 2.5 x ULN (performed within 28 days prior to day 1 of protocol therapy unless otherwise stated. In case of active disease, evaluation should be done within 15 days)

Alanine aminotransferase (ALT) =\< 2.5 x ULN (performed within 28 days prior to day 1 of protocol therapy unless otherwise stated. In case of active disease, evaluation should be done within 15 days)

Creatinine clearance of \>= 60 mL/min per 24 hour urine test or the Cockcroft-Gault formula (performed within 28 days prior to day 1 of protocol therapy unless otherwise stated. In case of active disease, evaluation should be done within 15 days)

Left ventricular ejection fraction (LVEF) \>= 50%

* Note: To be performed within 28 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 lung for carbon monoxide (DLCO) (diffusion capacity) \>= 50% of predicted (corrected for hemoglobin). If unable to perform pulmonary function tests: oxygen (O2) saturation \> 92% on room air.

* Note To be performed within 28 days prior to day 1 of protocol therapy

Seronegative for human immunodeficiency virus (HIV) antigen (Ag)/antibody (Ab) combination (combo), hepatitis C virus (HCV), active hepatitis B virus (HBV) (surface antigen negative), and syphilis (rapid plasma reagin measurement \[RPR\])

* If HCV positive, hepatitis C ribonucleic acid (RNA) quantitation must be performed

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. 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)

What this study is about