An assembly made up of a pump, a container and an augmented fluid-recirculating system for increased working fluid agitation, and a method of agitating a liquid within a container—as well as dispensing such a liquid from the container—where the liquid has been subjected to such augmented agitation prior to such dispensing. The pump cooperates with the fluid-recirculating system that includes an eductor such that the liquid resident within the container may be recirculated in a manner to promote its own agitation. In addition, air or a related fluid may be passively introduced upstream of the pump such that it also may pass through the eductor. In one form, the assembly defines a closed-loop system such that the air or other gas already present in the container may be introduced selectively, while in another form, the assembly defines an open-loop system that retrieves air from a local external environment. In either case, the introduction of such air or related gas may be selective, thereby permitting an operator to dictate if such air should be recirculated. In addition, the use of a diaphragm pump helps avoid damage to the portions of the pump that are exposed to a mixed phase fluid flow made up of the air and recirculated liquid.