A fuel injection supply system includes an intensifier cylinder having an intensifier piston configured to pressurize fuel in an intensifier chamber of the cylinder during a pressurizing stroke, and further configured to draw fuel into the intensifier chamber during a recharge stroke. A fuel rail receives pressurized fuel from the intensifier chamber, and supplies the fuel to a plurality of fuel injectors. A control unit controls switching of the intensifier piston between a pressurizing stroke and a recharge stroke, controlling recharge strokes of the piston to occur between two consecutive injection events of the plurality of fuel injectors. The common fuel rail may be hydraulically locked except during injection events of any of the plurality of fuel injectors, or during a recharge stroke of the piston. The intensifier piston may be controlled to perform a recharge stroke once during each engine cycle, or more than once during each engine cycle.