Oh my, what a nuisance! Let's hope it is a simple blockage in an accessible spot. If not it might be preferable to replace your system with an aerobic one which does not use a leech field (?) I have no idea of the cost comparison, however.
I had a room nearly destroyed by cats also when my son's cats visited while he was moving. I had to repaint and replace the flooring - fortunately there wasn't much breakable in there, so the cats just "marked their territory", in the room in which they were fed. Ycck!
