Sure, but saying “have an open relationship” is also anthropomorphizing. Also, sneaking around describes what happens much better. I don’t know what it looks like with birds, but with apes when a non-dominant male mates with a female, they have to sneak around to do it. If the dominant male catches the non-dominant male he’ll attack him.

Here’s an example from monkeys:

https://www.discovermagazine.com/planet-earth/monkeys-try-to-hide-illicit-hookups

I haven’t found articles about chimps and gorillas, but I remember it being similar.