Is it possible to have authentication codes of the same site across two or more 2FA apps at the same time?
Yes, it is... I have Google Authenticator, Authenticator Plus and Aegis installed and running... I have the codes for several sites in either 2 or all three of the apps without any issues. NOTE: I mainly use Aegis these days... the other 2 are "leftovers"
I stopped using Authenticator Plus because it stopped getting updates (last update Dec 2018).