@doollard just to be clear, BuddyPress is a WordPress plugin, and so BP uses the same database as your WP installation. Therefore:
– You can install BP in your first WP installation where you used DB prefix wp11_
– You can also install BP in your second WP installation where you used prefix bp77_
Now if you mean that you want to run one WP/BP installation using two databases, that would be in the world of DB experts/developers. If you’re going to take this on yourself, look at:
– https://codex.wordpress.org/Class_Reference/wpdb
– https://wordpress.org/plugins/hyperdb/faq/
