Title says it all:
Can I run Tinderbox 7 along with Tinderbox 8 on the same computer?
(without opening the same file at the same time in both TBX versions)
You can have multiple versions installed on your computer - I have v5*, v6, v7,v8** and the current v8 beta, all except the beta are in my apps folder. As you note, you don’t want to open the same file in two apps, and further i’d suggest avoiding having more than one version open at a time.
* I’m not sure if v5 still runs, at some point is won’t. It’s there as this Mac dates from 2013 and I don’t throw out apps that often
** respectively named: Tinderbox.app, TinderboxSix.app, Tinderbox 7.app, Tinderbox 8.app.
Be aware that using multiple versions may confuse macOS as to which app opens TBXs but that’s an OS rather than app issue.
You can keep different versions on your Mac, i.e. vN.x vs vN.y, but I’d advise keeping them in different locations, i.e. not both in your apps folder as I may help the OS figure out which is which.
For later readers. Whilst I keep older versions for reference/testing, most users don’t need anything but the current version. Ideally, just keep the current release (or last available under your licence) and replace it with the current version when able. If not using the current version, do make that plain when seeking help from support or here in the forums.