You probable could but the feed water would grow dirtier and dirtier so your filters would not last as long. I would think the money spent in replacement filters would be more than the money spent letting it run down the drain.
Kipass4130 has some good ideas on what to do with the waste water... Maybe he will chime in or you can do a search and read up.
I'll be honest, the waste water was one of my biggest hurdles to get over. It had nothing to do with money, it was the though of wasting 100's of gallons of water.
I'm trying to figure out how to water my lawn this summer with the waste water. I think it's going to be easy, I just need a large tub or tank, a pump and the room to do it. It may not run sprinklers but it will soak the grass.