This phase II trial studies how well adding axatilimab to standard of care (SOC) therapy works in preventing graft versus host disease (GVHD) following allogeneic hematopoietic stem cell transplantation (HCT) in patients with hematologic cancer. Allogeneic HCT is a procedure in which a person receives blood-forming stem cells (cells from which all blood cells develop) from a genetically similar, but not identical, donor. This is often a sister or brother, but could be an unrelated donor. Sometimes the transplanted cells from a donor can attack the body's normal cells, causing GVHD. Symptoms of GVHD can include yellowing of the skin, mucous membranes, and eyes, skin rash or blisters, dry mouth, or dry eyes. Typically, drugs such as cyclophosphamide, tacrolimus, and mycophenolate mofetil are given after the transplant to help stop GVHD from happening, but these current therapies may negatively affect patient quality of life and newer treatment strategies are needed. Axatilimab is a monoclonal antibody. A monoclonal antibody is a type of protein that can bind to certain targets in the body, such as molecules that cause the body to make an immune response (antigens), which may prevent GVHD from developing. Adding axatilimab to SOC therapy may be more effective in preventing GVHD following allogeneic HCT in patients with hematologic cancer.