While it is possible to clean and reuse grey water, I have not found a practical way to do it effectively for RVers. The problem is the amount and kind of sediment that is in the grey water. Food particles, soap, hair will quickly plug a sediment filter, so some kind of multi-stage filtration system would be needed. That said, there are many pretty creative solutions for recycling shower water, or just recirculating it so you use the smallest amount of water possible and still get a nice hot shower. There are some DYI solutions I have seen for reusing shower water. Below are a couple links that I have found for some ideas.