Allogeneic CD56-positive CD3-negative Natural Killer Cells(MD Anderson Cancer Center)

This phase I/II trial studies the side effects and best dose of donor natural killer cells when given together with donor stem cell transplant and to see how well they work in treating patients with myeloid malignancies that are likely to come back or spread. Giving chemotherapy, such as busulfan and fludarabine phosphate, before a donor peripheral blood stem cell transplant helps stop the growth of cancer cells. It may also stop the patient's immune system from rejecting the donor's stem cells. When the healthy stem cells and natural killer cells from a donor are infused into the patient they may help the patient's bone marrow make stem cells, red blood cells, white blood cells, and platelets.