Trial of Scheduled Versus Treatment Administration of Donor-Derived Viral Specific T-cells for Viral Infections After Stem Cell Transplant

This study is testing whether giving donor immune cells (called virus-specific T cells, or VSTs) on a set schedule — before any viral infection develops — is better than waiting until a viral infection occurs after a bone marrow/stem cell transplant. **You may be eligible if...** - You have recently received a bone marrow or stem cell transplant (at least 21 days ago) - Your overall health is stable enough to receive the VST infusion - You are not on high doses of steroids - OR, in the treatment arm, you have a detected viral infection (adenovirus, CMV, EBV, or BK virus) above a certain threshold level in your blood **You may NOT be eligible if...** - You have active severe graft-versus-host disease (GVHD, a complication where donor cells attack the recipient's body) - Your original cancer is relapsing in an uncontrolled way - You received certain immune-suppressing antibody treatments (ATG or alemtuzumab) very recently - Your condition is too critical to safely receive the infusion Talk to your doctor to see if this trial is right for you.