A wet press for forming molded fiber products includes a slurry tank for holding a pulp slurry, and a forming platen for holding a forming die having a porous forming surface. The forming platen is movable between a dipping position proximate the tank and a pressing position spaced apart from the dipping position. The wet press further includes a transfer platen for holding transfer tooling having a first transfer face and a second transfer face. The transfer platen is movable for selectively positioning each of the first transfer face and the second transfer face in alignment with the forming platen when the forming platen is in the pressing position.