Adding Itacitinib to Cyclophosphamide and Tacrolimus for the Prevention of Graft Versus Host Disease in Patients Undergoing Hematopoietic Stem Cell Transplants

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)