A system includes a turbine having an exhaust flow path through a plurality of turbine stages, wherein the plurality of turbine stages is driven by combustion products flowing through the exhaust flow path, at least one main combustor disposed upstream from the turbine, wherein the at least one main combustor is configured to combust a fuel with a first oxidant and an exhaust gas to generate the combustion products, at least one reheat combustor disposed in or between turbine stages of the turbine, wherein the at least one reheat combustor is configured to reheat the combustion products by adding a second oxidant to react with unburnt fuel in the combustion products, and an exhaust gas compressor, wherein the exhaust gas compressor is configured to compress and route the exhaust gas from the turbine to the at least one main combustor along an exhaust recirculation path.