An appliance comprising a dispensing system and a downstream assembly, wherein the dispensing system is configured for dispensing fluid to the downstream assembly, the dispensing system comprises: a housing defining a chamber; a piston movable within the chamber of the housing between a first position and a second position, the piston fluidly separating a first reservoir and a second reservoir of the chamber; a first inlet conduit configured to be in fluid communication with a water supply and the first reservoir of the chamber; a first valve positioned along the first inlet conduit and movable between an open position and a closed position, the first valve configured to selectively allow fluid to flow from the water supply to the first reservoir of the chamber; a second inlet conduit configured to be in fluid communication with the water supply and the second reservoir of the chamber; a second valve positioned along the second inlet conduit and movable between an open position and a closed position, the second valve configured to selectively allow fluid to flow from the water supply to the second reservoir of the chamber; a first outlet conduit in fluid communication with the first reservoir of the chamber and the downstream assembly; a third valve positioned along the first outlet conduit and movable between an open position and a closed position, the third valve configured to selectively allow fluid to flow from the first reservoir to the downstream assembly; a second outlet conduit in fluid communication with the second reservoir of the chamber and the downstream assembly; and a fourth valve positioned along the second outlet conduit and movable between an open position and a closed position, the fourth valve configured to selectively allow fluid to flow from the second reservoir to the downstream assembly, characterized in that the downstream assembly is an ice making assembly and the appliance is a refrigerator appliance. a housing defining a chamber; a piston movable within the chamber of the housing between a first position and a second position, the piston fluidly separating a first reservoir and a second reservoir of the chamber; a first inlet conduit configured to be in fluid communication with a water supply and the first reservoir of the chamber; a first valve positioned along the first inlet conduit and movable between an open position and a closed position, the first valve configured to selectively allow fluid to flow from the water supply to the first reservoir of the chamber; a second inlet conduit configured to be in fluid communication with the water supply and the second reservoir of the chamber; a second valve positioned along the second inlet conduit and movable between an open position and a closed position, the second valve configured to selectively allow fluid to flow from the water supply to the second reservoir of the chamber; a first outlet conduit in fluid communication with the first reservoir of the chamber and the downstream assembly; a third valve positioned along the first outlet conduit and movable between an open position and a closed position, the third valve configured to selectively allow fluid to flow from the first reservoir to the downstream assembly; a second outlet conduit in fluid communication with the second reservoir of the chamber and the downstream assembly; and a fourth valve positioned along the second outlet conduit and movable between an open position and a closed position, the fourth valve configured to selectively allow fluid to flow from the second reservoir to the downstream assembly, characterized in that the downstream assembly is an ice making assembly and the appliance is a refrigerator appliance.