The present invention provides a medical liquid administration apparatus and administration method that are particularly apt for intravenous (IV) applications. More particularly, the administration apparatus and method may be employed in conjunction with the administration of liquid medication and one or more flush solutions from multi-dose sources, wherein fluid interconnections between at least one flush solution source and the administration apparatus may be established a single time at the outset of a given procedure. The administration apparatus may include a valve having a control member selectively positionable to provide any selected one of a plurality of closed flow paths through the valve, and a syringe interconnected to the control member for clockwise/counterclockwise co-rotation therewith (e.g. to establish the selected flow path).