A pump module (50) is provided for use in a medical fluid dispensing system thatincludes a pump body (52) made of a non-compliant material and first (54) and second(56) pump chambers formed in the body. Each of the chambers has a first, open end(58) and an opposite, closed end (60). The pump module (50) further includes first(68a) and second (68b) pistons in the first (54) and second (56) pump chambers,respectively. At least one fluid inlet (90a) and a fluid outlet (90c) are selectivelyin fluid communication with the first (54) and second (56) pump chambers. Eachof the pistons (68a, 68b) extends through the open end of a respective one of thepump chambers (54, 56), with each of the pistons (68a, 68b) being operably translatablewithin the pump chamber toward and away from the closed end (60, 64) of the chamber.The pistons are translatable independently of one another.