Changing my theme without going down

I would like to change my theme. I know that there will be a lot of work to do during this changeover and I was wondering whether there’s a way to work on the new theme in some kind of isolated fashion, while the old theme is up and running.

I wouldn’t post anything on the old theme while working on the new so that the content would stay the same.

Then, when the new theme is all set up to my liking I’d make the switch so my visitors will see the new setup.

Is this possible?

Thanks,
Martin