A modular press assembly for performing multiple position pressing with a single press. The modular press assembly includes a floating mount attached to the upper platen of the press, a hydraulic cylinder, and a press ram coupled to the cylinder which automatically guides itself precisely into axial alignment with a die situated on a lower platen and containing material to be pressed. A plurality of such press assemblies are mounted on the upper platen and are connected through respective flow control valves to an independent hydraulic control system to allow adjustment of the travel of the multiple press rams. This configuration facilitates multiple position pressing and equally divides the total press force from the single hydraulic press, distributing it among each of the multiple positions independent of the final height of each pressed body.