Hey l4xam,
It would only be possible to be signed into one Apple ID at a time on your iPhone.
You can learn more about Game Center here: Use Game Center to play with friends - Apple Support
"Create a Game Center profile
Learn how to create a profile with a personalized Memoji and customized initials.
On your iPhone or iPad
- Open Settings. Scroll to Game Center, then tap it.
- If Game Center isn’t on, turn it on, then sign in with your Apple ID.*

- Tap the Nickname field to enter a name that your friends will see when you play games together. If you can’t think of a name, you can choose one of the randomly generated suggestions.
- To personalize the picture that shows with your nickname, tap Edit in the circle at the top of the page. From here, you can create a Memoji, use an existing one, or customize how your nickname's initials appear.
* If you see a nickname or other information already set up, you might already have a Game Center profile. To verify that you're signed in with your Apple ID on your iPhone or iPad, go to Settings and look for your Apple ID. To verify that you're signed in with your Apple ID on your Mac, choose Apple menu > System Settings, then click Internet Accounts and look for your Apple ID in the sidebar."
Thanks!