Alpha/Beta T Cell and CD19+ B Cell Depletion in Allogeneic Stem Cell Transplantation in Patients With Malignant Diseases

This study is testing a special type of stem cell transplant for children, teens, and young adults with blood cancers. The transplant uses donor stem cells that have been carefully filtered to remove certain immune cells, which may reduce the risk of serious complications after transplant. **You may be eligible if:** - You are between 6 months and 39 years old - You have a blood cancer such as acute leukemia (ALL or AML), juvenile myelomonocytic leukemia, CML, high-risk myelodysplastic syndrome, or lymphoma (Hodgkin or Non-Hodgkin) - Your cancer is high-risk, in second remission or beyond, or did not respond well to initial treatment - A matching donor (related sibling, unrelated donor, or half-matched family member) is available - Your heart, lungs, kidneys, and liver are functioning well enough **You may NOT be eligible if:** - You have an active, uncontrolled infection - You had a stem cell transplant from a donor within the last 6 months - You have active graft-versus-host disease (a reaction where donor cells attack your body) - You are pregnant or breastfeeding - You are currently incarcerated Talk to your doctor to see if this trial is right for you.