It is possible to connect to one server, quickly cancel and immediately connect to anoher server, to get into both of them with the world being in one of them, and the chat/permissions being on the other server. I was able to enable fly mode on the server I'm operating (90gQopen) while logging into the world of Parkour, so I was able to fly in adventure mode on that vanilla server.

This is reproduceable on two vanilla servers as well.

It is also possible to do this by selecting one of the servers and hovering the "Play" button on the other one, and at the same time hit enter and click on the play button, to get into both of the servers but it's a lot harder.

How to reproduce it: https://www.youtube.com/watch?v=tIwN9mwCvzM
The video is unlisted.