A system includes a turbine combustor having a first volume configured to receive a combustion fluid and to direct the combustion fluid into a combustion chamber and a second volume configured to receive a first flow of an exhaust gas. The second volume is configured to direct a first portion of the first flow of the exhaust gas into the combustion chamber and to direct a second portion of the first flow of the exhaust gas into a third volume isolated from the first volume. The third volume is in fluid communication with an extraction conduit that is configured to direct the second portion of the first flow of the exhaust gas out of the turbine combustor.