Pomalidomide for Chronic Graft-versus-Host Disease

Background: \- Pomalidomide is a drug that alters the body's immune response. It may help people who have chronic graft-versus-host disease (GvHD). GvHD may appear after a stem cell transplant, when immune cells in the transplant try to attack tissues in the person who received the transplant. GvHD is not easy to treat, and often does not respond to standard treatments. Researchers want to see if pomalidomide is a safe and effective treatment for GvHD. Objectives: \- To test the safety and effectiveness of pomalidomide for GvHD that has not responded to standard treatments. Eligibility: \- Individuals at least 18 years of age who have GvHD that has not responded to standard treatments. Design: * Participants will be screened with a physical exam and medical history. Blood and urine samples will also be collected. A lung function test and imaging studies will also be given. * Participants will take pomalidomide capsules once a day for 4-week periods called cycles. * Treatment will be monitored with frequent blood tests and imaging studies. Saliva samples and skin and mouth tissue biopsies will also be collected during treatment. * Treatment will continue for six cycles (6 months), unless the GvHD gets worse or side effects are too severe. If the GvHD has improved at the end of the six cycles, participants may be able to continue to take pomalidomide for up to six more cycles.