One of my cats soils outside of the litter tray on a regular basis. I think this is because she doesn't like sharing with another cat.
No matter how many litter trays we use, as soon as we have cleaned them our neutered male cat will use each one! So then when our female cat wants to use one she doesn't want to because he's already been in!
I know you can get cat flaps that are magnetised and that only one cat can get through due to a magnet on their collar. Is there anything similar with regard to litter trays?