RecruitingPhase 1Biological interventionDonor T Cell Therapy in Treating Immunocompromised Patients With Adenovirus-Related DiseaseThis phase I trial studies the side effects of allogeneic adenovirus-specific cytotoxic T lymphocytes (donor T cell therapy) and to see how well they work in treating patients with a weakened immune system (immunocompromised) and adenovirus-related disease. Allogeneic adenovirus-specific cytotoxic T lymphocytes are made from donated blood cells grown in the laboratory and are designed to kill viruses that can cause infections in immunocompromised patients with adenovirus-related disease.