A water-on-water filtration system that includes a filter member and two storage vessels. The system includes a plurality of valves that are controlled to place a first of the storage vessels in a fill state in which the first storage vessel is being filled with filtered water, and concurrently place the second of the storage vessels in a service state in which filtered water held in the second storage vessel is delivered as an output of the filtration system. The filtration system can be configured to supply a constant output of filtered water to meet a constant demand while using a relatively small filter member and relatively small storage vessels.