Transfer games to another Apple ID

I have a game with progress on one Apple ID, synced to their Game Center account. I recently set up a new Apple ID and want to transfer my games to the new ID.

I know that with Android devices, I can just sign out of my current account and sign in with my new account, and all the games, in-app purchases, and game data will be loaded to the new account. Can I do this with Apple ID?

If I can't, how else can I transfer my games?