How does this work on ios? In my experience, a phone can only have one apple ID at a time.

Sign out of the app store. Sign in with a different ID. Install the app you want. Sign out again.

The apple ID used for the app store doesn't have to be the same as the apple ID for Facetime, Messages etc. You don't even need to be signed in to the app store to use an app that's already installed.

Oh cool. I didn't realize that was possible. I have most of my apps still from when I lived in the US in my history, so downloading them again isn't an issue, but if I need another one, I will definitely try this out!