A fuel cell system has: a fuel cell having a first reactant inlet, a first reactant outlet, a second reactant inlet, a second reactant outlet, and optionally a coolant inlet and coolant outlet. A first reactant supply subsystem supplies a first reactant incoming stream to the first reactant inlet of the fuel cell. A second reactant supply subsystem supplies a second reactant incoming stream to the second reactant inlet of the fuel cell. A first reactant recirculation subsystem recirculates at least a portion of the first reactant exhaust stream from the first reactant outlet to an enthalpy shifting subsystem in which one portion of the heat and moisture in first reactant exhaust stream is transferred to one of the first reactant incoming stream in the first reactant supply subsystem and the second reactant incoming stream in the second reactant supply subsystem. Another portion of the heat and moisture is transferred to the other stream. A method of controlling reactant and water in a fuel cell system is also disclosed.