Modular medical fluid management assemblies and associated machines and methods

Medical fluid management assembly includes: a pneumatic manifold including multiple plates forming pneumatic passageways, a pneumatic valve chamber and a pneumatic pump chamber, the valve chamber in pneumatic communication with at least one passageway, the pump chamber in pneumatic communication with at least one passageway; and a fluid manifold including multiple fluid pathways, a fluid valve chamber in selective fluid communication with a fluid pump chamber and at least one fluid pathway, wherein (a) the pneumatic valve chamber and the fluid valve chamber are mated together to compress a membrane and (b) the pneumatic pump chamber and the fluid pump chamber are mated together to compress a membrane, wherein at least one of the pneumatic valve chamber or the pneumatic pump chamber extends from the at least one plate, or the fluid valve chamber or the fluid pump chamber extends from the fluid manifold to aid in compressing the membranes.