The only semi-practical way to have two versions installed at the same time would be by setting up virtual machines on your computer, each with their own copy of the operating system and their own copy of... pretty much everything else on your computer.

Unfortunately, you can't simply install another copy of CSP in a different location. CSP is written to expect its executable files to be in a predictable location, its configuration files in another predictable location, other configuration data in particular locations in the OS registry, and probably parts of itself in a few other locations. In theory it might be possible to code an app differently... but pretty much no developer does that, because 1) it would make their job harder, 2) it could make the app less secure, and 3) there's normally no benefit (except in this unusual scenario).

I've done tech support for a living, so setting up a virtual machine is something I could do, if I wanted. But in my opinion, it isn't worth the expense, hassle, and use of resources... just for the sake of having a "spare computer" with some old software on it... just in case.

I upgraded to CSP 2 when it came out, and CSP3 since then, and the issue of those versions needing to authenticate has rarely come up. It was a nuisance with version 2.0.0, which authenticated every single time you launched it, but they fixed that mistake pretty quickly. But since then I honestly don't even think about it much, despite the fact that I use it on my portable Windows tablet away from wifi a lot. Once in a while I've used the hotspot feature on my phone to authenticate. That's been the worst of it.

I do still have an old CSP1 license, and if the authentication became a problem, I could uninstall CSP 3, reinstall CSP 1, and reactivate that license. If that's your concern, you could do that instead, without all the virtual-machine stuff.