A high sided litterbox would work better. My parents have a litterbox with a detachable rim that slants inwards to keep the litter in. They don't use it anymore. One of their cats likes to pee only in the corners of litterboxes and with that box he would stick his rear end over the rim and would end up peeing outside the box. The other cat just didn't like it and would scratch at it.
Actually, I have switched to that type of litter box. The boys used to go for distance kicking the litter all over the laundry room. Since i got the rimmed litter box, they don't mess up the floor anymore. It all stays in the box! The rim lifts off as well if you want to put liners in the box - I tried that and didn't like it because the boys took great pleasure in scratching the bejesus out of the liners and putting holes in them, rendering them useless anyway! A little bit of a game for them!
I like my litterbox with the rim...it does help keep the litter inside the box! I have several covered litterboxes, and a giant litterbox made from a rubbermaid container, too!
My Chynna is a shoveler and I swear she would dig her way to China if it weren't for the plastic bottom of the box, LOL Every time she would use the box 1/2 the litter would end up on the floor
I bought one of those with the rims. The rims are attached and just connect with plastic locking pins in the corners. When I clean the box I just pop open the pins and fold the sides back and then just fold them back over when done.
It sure has helped with the shoveling problem. And it's also helped keep the urine in the pan for the most part. My cats are "edgers" and love to pee along the side of the pan. Before I got this rimmed pan, about 1/2 the time they were over shooting the side. Now it only happens occasionally.
I love the rimmed litter boxes. Smudge is a messy girl. SHe loves to make a pile of litter outside the box for me to clean up. The rims now prevent her from doing that. Jus tmake sure that you clean the underside of the rims especially well. If not, mold can grow on them. Neighbors of mine have had that problem.
I've had the same results with a rimmed box. Gizmo likes to use the edges, and once in a while she does an 'up and over' move out of the box, but usually she does fine with the high sided, two-part box.