Ruxolitinib With and Without CTLA-4 Ig Abatacept for the Prophylaxis of Graft-Versus-Host Disease and Cytokine Release Syndrome After T-cell Replete Haploidentical Peripheral Blood Hematopoietic Cell Transplantation

Inclusion Criteria: Patients must meet the following criteria within 30 days prior to Day -3 unless otherwise noted. * Diagnosis of one of the hematological malignancies listed below: * Acute myelogenous leukemia (AML) in complete morphological remission, complete remission with incomplete hematologic recovery, and complete remission with partial hematologic recovery (based on ELN Criteria47). * Acute lymphocytic leukemia (ALL) in complete morphological remission (MRD negative by flow cytometry with sensitivity to ≤ 10-4). * Myelodysplastic syndrome with ≤ 10% blasts in bone marrow. * Non-Hodgkin lymphoma (NHL) or Hodgkin lymphoma (HD) in second or greater complete or partial remission. * Myelofibrosis with ≤ 10% blasts in bone marrow. Up to five patients with myelofibrosis will be permitted in Regimen 1 and up to five in Regimen 2. * AML in partial response. One patient will be enrolled in Regimen 1 given the prospect of potential benefit. * Planned treatment is T cell-replete peripheral blood haploidentical donor transplantation. * Available HLA-haploidentical donor who meets the following criteria: * Blood-related family member, including (but not limited to) sibling, offspring, cousin, nephew, or parent. Younger donors should be prioritized. * At least 18 years of age. * HLA-haploidentical donor/recipient match by at least low-resolution typing per institutional standards. * In the investigator's opinion, is in general good health and medically abl…