Is it possible to have an old version of Xcode installed at the same time as a newer version of Xcode is installed?

Yes, in some examples. Rename the old one, before manually installing the new from here: https://developer.apple.com/download/more/

Just be aware that both will use the same prefs plist when running, so don't be surprised if things get co-mingled. I would not run them both at the same time, and, be careful using the same project with both... certain changes might occur that cause conflicts.

If you open a project in new, then old, the old may complain that the project isn't compatible. This can be changed in settings, but not unless you are comfortable with that type of change. As always, be sure to have a tested and reliable backup in place at all times.

I think the usual example of two versions installed simultaneously is release and beta.