This was fun, Deborah.
We have never had more than three kitties at the same time.
In each case, the third cat always claimed the library for his/her spot. The others could come and share for a bit, but whoever was in charge of the library, was the defacto owner, and there were no disputes.
The only one who ever pushed the boundaries, was Gandalf. He would just quietly insert himself onto the shelf/bd and be there. No hissing or grumbling. The other cat might glare at him, but since he would not respond, nothing came of it,