Why do you think that people don't love more than one person at a time? That's the plot of every Rom-Com ever. Maybe that's true for you, but it's certainly not the norm. Plenty of people still love their exes as well as their current partners. There are also lots of different kinds and forms of love, and I don't love all my partners in exactly the same way, but where is the rule that you have to?

And yes, loving multiple people (cats) platonically is exactly the same thing as loving multiple people romantically/sexually. It's just that you've been taught that the latter is not possible - which is the whole point of this OP.