You can have both the trial and your purchased spine version, otherwise as far as I know, not.
What I do as a workaround is having them in two different partitions of windows, so in one I can have the beta, in the other one I have the latest stable release.
Rolling back Spine is not hard either (just click on the spine logo, settings... and choose a different version of spine from the first context menu). You need to restart Spine to see the effects. With this method you could keep on switching between versions, although it's a bit cumbersome.

Probably by different versions, he means versions of the editor. Yes, you can run different versions of Spine on the same computer:
Settings - Spine User Guide: Version

I assume the use case is to run different versions in parallel, which is currently not supported (save for the Trial vs. purchased Spine hack Erikari mentioned).

I hate when we have to guess the problem. Next time let's just ask for more info!