I think my high peer Princess does so due to her age, she's about 12 years old. She still runs and plays but she's definitley slower than she used to be and the high peeing didn't start up until a couple of years ago. The litter box we have now is good but she comes dangerously close to peeing on the rim sometimes. It's ok for now and if she starts peeing over it I will probably get a sterilite or any mentioned above.