A dishwasher with for treating dishes according to a cycle of operation. The dishwasher has a chassis comprising a base on which is supported a open-faced tub, which at least partially defines a treating chamber; a closure selectively moveable between and an open position and a closed position to selectively open and close the open-faced tub, a controller for selectively controlling the cycle of operation of the dishwasher, and a dispenser assembly comprising an engagement assembly in communication with the controller; the engagement assembly operably coupled with at least one of a dispensing device and one or more dispensing cartridges to adjust the position of one of the dispensing device and/or the dispensing cartridges to selectively dispense treating chemistry from the selected dispensing cartridge.