cats doing the litterbox shuffle

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When I saw my cat, Waffles, stepping into a litterbox used by Mimi, my newest addition, I shooed her away. After all, there are two existing litterboxes around, one in the kitchen and the other in the sunporch. The present location of Mimi's litterbox is temporary, as it is in my computer room where the floor is covered by an old rug. If my other two cats start using Mimi's litterbox, they may inadvertently pee on the rug, something I want to avoid. There is no way to permanently get rid of cat pee or its odor. Plus, the last thing I need is yet another litterbox to clean, like I don't have enough to do. So, am I so wrong for stopping Waffles from peeing in Mimi's litterbox? (Waffles peed in the kitchen litterbox later on.) Mimi is still getting acclimated to her new home and I don't want her to avoid using her own litterbox if another cat has peed in it. Or is my imagination just working overtime? After all, cat pee is cat pee, or is there a difference between one cat's pee and another's?