BuddyPress.org

Always check through the Documentation first off as theres often help and guides to be found for common issues.

You might find this helpful for starters :
https://codex.buddypress.org/getting-started/install-buddypress-on-a-secondary-blog/

=== So it wouldn’t necessarily be just a secondary blog, it would be every blog created on WP multisite. ===

Understood. That scenario is not possible at this time – only one BP instance in main or secondary blog for multisite installation.

== Is it possible to just install a new version of buddypress on each subsite so each subsite will have its own version of buddypress? ==

If you install WP at http://www.yoursite.com/ and go multisite – either http://yoursite.com/subsite1 (for subdirectory) or http://subsite1.yoursite.com/ (for subdomain) – that subsite is what’s meant by a secondary blog. And that brings us back that there can be only one BP instance in main site or subsite of a multisite installation.