A high efficiency fuel cell system includes a topping fuel cell assembly including a topping cathode portion and a topping anode portion, a bottoming fuel cell assembly including a bottoming cathode portion and a bottoming anode portion, wherein the bottoming anode portion receives anode exhaust output from the topping anode portion, and a separation assembly configured to receive carbon dioxide-containing exhaust and to separate carbon dioxide from the carbon dioxide-containing exhaust, wherein at least one of the topping cathode portion and the bottoming cathode portion receives at least a portion of flue gas output from a flue gas generating device, and wherein the topping fuel cell assembly has a greater number of fuel cells than the bottoming fuel cell assembly so that the topping fuel cell assembly utilizes more fuel than the bottoming fuel cell assembly.