The present invention involves several different embodiments related to a crossover switching valve. The crossover switching valve is preferably designed to receive fluid from a reservoir, or other fluid source, and direct the inflow and outflow of the fluid between the valve and one or more pumps. In one embodiment, the valve is configured to provide a substantially continuous flow rate when used in connection with a double acting pump. In another embodiment, the valve preferably includes an inflow port, an outflow port, and first and second ports configured to be fluidly connected to at least one pump. Another embodiment of the present invention is a conduit that preferably provides fluid communication between the first and second ports. Yet another embodiment is a fluid director that is preferably configured to alter flow of fluid through the conduit. In some embodiments, the inflow port is in fluid communication with the first port while the outflow port is in fluid communication with the second port. In other embodiments, the inflow port is in fluid communication with the second port while the outflow port is in fluid communication with the first port. Also disclosed is a pumping system that incorporates the crossover switching valve and a pump.