Can I maintain two versions of my site?

I have made a (calendar) app which is now perfectly usable and performs well enough so that I would like a handful people to start using it every day and provide feedback... However there are still many additional features I would like to add. This means that there will be lots of times when the site will be down because I'm half way through trying out new code. What I'd like to be able to do is set up two versions of the site, a "release" one for my testers and a "development" one for me to work on. Can this be done in any way with the free "beginner plan"?

No, you can only have one web app, so there would be no way to test the site that you're working on while your actual web app is running.