I got a weird problem involving both of my cats (Siegfrieda, to the left; Kika, to the right).
Kika is rather particular about having her own litterbox(es), and refuses to use a litterbox shared by another cat. Frieda on the other hand is adept to the "if I fits, I sits, I shits" philosophy, and is totally OK sharing litterboxes.
That creates a problem: no matter if properly and regularly cleaned, the only one using litterboxes here is Frieda. We had, like, five of them at once; and Kika would still rather do her business on the patio.
How do I either teach Kika "it's fine to share a litterbox", or teach Siegfrieda "that's Kika's litterbox, leave it alone"?
I see you mentioned elsewhere that automatic boxes probably won't be sufficient. While I generally wouldn't recommend a litter box that fully disposes of the waste automatically (because scooping the poop might be the first or only warning sign of health issues), something like the Cat Genie might help.
If Kika is willing to use an enclosed litter box, you might create a litter box enclosure using one of those pet doors that can be set to unlock only for specific animals based on their microchip or a collar tag.