MiniBB allows to run multiple forums on the same core and scripts.
Regarding the sub-domain the script is called from, you could operate this condition and in setup_options.php provide a boolean code to load different values for database settings/table names, files path, cookies etc. Then instead of the default database, miniBB will load different database - but still, it will work on the same core. So when upgrading, you could upgrade all forums at once. This is the best and supported approach.
The approach described above, is used in Archiving feature
of miniBB-based forum.
Copying yet another version of the software is not the best approach. It would work only if you have a completely different forum, with the different layout, add-ons, functionality and so on. Then you will be forced to upgrade 2 versions at once, i.e. it will take you double time for 2 forums, triple time for 3 forums etc.