We'll have at least 2 entry/exit points though we only have the one cat. We want to give him space that's his, away from the dog (who has never lived with a cat before). As silly as it sounds, the apartment is not that large, so I am concerned that a deeper catwalk than 8 inches may make the room feel very enclosed. I'm planning, as we have more money once I get a job and so on (which will take some time after the move) to add some platforms to the catwalk in the corners for lounging and toys. He'll also have the tops of a bunch of different furniture--shelves and our tv stand is a deep (maybe 18 or 20 inches?) shelf. The catwalks are primarily to give him space that he can get around the room to where he wants to go without his little toesies ever hitting the ground where the dog is, in case she turns out to be a bit too interested in him. She's seen cats and seemed all right, but she's never had 24 hour access to one.
With time, the network will be expanded for him. I probably should have said that in the OP. This is just the basic design, at present.
The advanced (longterm) design? I'm planning to put stolmen (an Ikea vertical tension rod) based cat shelving in some of the corners. I'm planning to add 'catwalks' to the fronts of some of the bookshelves to give him extra lounging space there. If I can figure out a way to support it without doing too much damage to the flat (especially the ceiling), I'm planning to put a cross-beam across the middle of the room that will be wider, for lounging and observing purposes. With time, there may also be hidey-boxes on the walls. Basically, once I get a job in the US and am able to contribute financially, the idea is for him to get a new climby/loungey every few months, to build up our collection so that when we move to a larger place after my partner finishes her PhD, we'll be able to furnish the whole thing as an epic cat paradise for Peter and a friend (probably he will get a friend after I move down as he has never been a solo cat in his life--we've always lived with roommates who had cats and he was a trap from a feral colony that turned out to be snuggly so he got adopted out rather than being released after his neuter). We're thinking about getting a bengal to be his buddy, so we'll want lots of kitty superhighway in the apartment for playful Peter and his potential bengal buddy.