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

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
* 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)

Exclusion Criteria:

* Chemotherapy, radiation therapy, biological therapy, and/or 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
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to study agent
* Psychological issues, no appropriate caregivers identified, or non-compliant to medication
* Uncontrolled medical or psychiatric disorders which may preclude patients to undergo clinical studies (Discretion of the attending physician)
* Active diarrhea due to inflammatory bowel disease or malabsorption syndrome
* Clinically significant uncontrolled illness
* Active, uncontrolled systemic infection (bacterial, viral, or fungal) requiring antibiotics
* Known history of immunodeficiency virus (HIV) or hepatitis B or hepatitis C infection
* Diagnosis of Gilbert's disease
* 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)