Safety and Efficacy of Abatacept for Treating Chronic Cytopenia in Cytotoxic T-Lymphocyte Antigen 4 (CTLA4) Haploinsufficiency

Background: CTLA4 stands for cytotoxic T-lymphocyte antigen-4. It is a protein the body makes naturally to check its immune system from attacking itself. Some people don t produce enough CTLA4 protein, causing problems due to overactive immune system such as big spleens, repeated lung infections, breathing problems, stomach and intestine symptoms as well as inflamed brain and nerve problems. Many have problems with their bone marrow causing low numbers of blood cells like platelets, red blood cells or white blood cells, which is called cytopenia. Researchers want to see if the drug abatacept can treat cytopenias by replacing the missing protein CTLA4. Objective: To see if abatacept is safe and helps treat cytopenias caused by CTLA4 deficiency. Eligibility: People ages 8-65 years who have CTLA4 deficiency with cytopenia Design: Participants will be screened with medical history, medication review, physical exam and blood and urine tests. They will continue their current medications and may start taking antibiotics daily. Participants will receive either abatacept or placebo through a vein for 6 months. The study team will not know if you are receiving the study drug or the placebo Women who can become pregnant must agree to use birth control measures. Men who get someone pregnant during the study will be asked to collect information and have the partner contact the study team. Participants will undergo the following procedures before starting the study and at the completion: * radiology scans of body and brain * heart and lung function tests * Bone marrow examination by a needle inserted into the hip bone to remove a small amount of tissue to study. * Participants may have a small camera on a long, thin tool passed down the throat into the stomach and small intestine for evaluation of their gut. * Questionnaires about their disease, symptoms and quality of life Over 6 months, participants will have regular study visits and get 8 doses of the study drug or a placebo by intravenous injection. They will repeat some of the same tests done earlier at the end of the study at assess response. About 1 month after the last study drug visit, participants will have a final study visit. Some participants may join a treatment extension for the study drug abatacept with no placebo. They will sign a separate consent form for this.