2FA Backup on Changing Devices

Hello all!

I have 2FA using an authenticator app for a few different accounts, and I am trying to figure out a way that I could use different devices and retain access to the codes to log into those accounts. Currently, if I wanted to my phone to a different device,, I would have to deactivate 2FA on these accounts and set it up again using an authenticator app on my new device.

Is there any way to back up the codes so that regardless of what device I am on, the 2FA login codes are the same and all I have to do is log into one "master" account?

I may have a fundamental misunderstanding of how 2FA works, so I apologize if this is a silly question. I'm just looking for something to improve QOL while using these codes.

Thank you in advance!