If you did make such a system:
I would use a booster pump with a pressure shutoff switch, have it feed through a check valve into a pressure storage tank. Then have that side of the system connected into the filter input using a tee. That pressure tank would reduce pump cycling. Probably gravity feed the input of the pump so as to prevent any sort of air lock. Youd also want a float switch in the dirty water tank to shut the pump down when the water level is low.
All this would be to reuse about a third of the water.