Brief Summary: This phase II trial studies how well itacitinib works in preventing graft versus host disease in patients with blood disorders undergoing donor stem cell transplantation. A donor transplantation uses blood-making cells from a family member or unrelated donor to remove and replace abnormal blood cells. Graft versus host disease is a reaction of the donor's immune cells against the patient's body. Itacitinib plus standard treatment may help prevent graft versus host disease in patients who have received a donor stem cell transplantation.

Detailed Description: PRIMARY OBJECTIVE: I. To estimate the graft-versus (vs.) host disease-free/relapse free survival (GRFS) rate of itacitinib used as prophylaxis to prevent graft versus host disease (GVHD) after allogeneic stem cell transplantation (ASCT) at one year. SECONDARY OBJECTIVES: I. To assess the time to neutrophil and platelet engraftment and compare between matched and unmatched donors. II. To assess safety of itacitinib as measured by non-relapse mortality (NRM) at day 100. III. To assess the toxicity profile associated with this regimen. IV. To assess the incidence of acute and chronic GVHD. V. To assess the incidence of disease relapse. VI. To assess the incidence of non-relapse mortality. VII. To assess overall survival and progression-free survival. VIII. To assess the incidence of withdrawal syndrome in patients with myelofibrosis. TERTIARY OBJECTIVES (CORRELATIVE STUDIES): I. To study immune recovery and cytokines at various time points pre and post-transplant. II. To study deoxyribonucleic acid (DNA) damage studies in various cells post-transplant. OUTLINE: CONDITIONING CHEMOTHERAPY: Patients receive busulfan intravenously (IV) over 3 hours on days -20, -13, and -6 to -3, and fludarabine IV over 1 hour on days -6 to -3 in the absence of disease progression or unacceptable toxicity. ALLOGENEIC STEM CELL TRANSPLANTATION: Patients undergo ASCT on day 0. GVHD PROPHYLAXIS: Patients receive itacitinib orally (PO) once daily (QD) on days -21 to 80. Patients with no evidence of GVHD at day 80 receive a tapered dose of itacitinib until day 90. Patients also receive tacrolimus IV then PO twice daily (BID) for 3 months when able, and methotrexate IV over 30 minutes on days 1, 3, and 6 (day 11 also for patients with a matched unrelated donor). After completion of study treatment, patients are followed up at 100 days, 6 months, and 1 year.