This phase II trial studies how well donor cellular therapy after cytarabine works in treating patients with intermediate-risk acute myeloid leukemia with a decrease in or disappearance of signs and symptoms of cancer. Donor cellular therapy is a short-term transfusion of cells from a family member who is incompletely matched. The use of these partially matched white blood cells may help improve response to standard chemotherapy (cytarabine) and reduce some of the risks of infection, without a permanent transplant. Drugs used in chemotherapy, such as cytarabine, work in different ways to stop the growth of cancer cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving donor cellular therapy after cytarabine may kill more cancer cells.