Absolutely. While JFBConnect is a great extension (and I'm completely biased of course), our support is where we really shine.
Basically, to do what you're saying, you'd need 2 Joomla installations, and 2 databases. We actually have multiple Joomla sites running on sourcecoast.com:
www.sourcecoast.com
www.sourcecoast.com/jfbconnect/
www.sourcecoast.com/jfbconnect/demo
While it's not necessary to have 3 different sites for what we do, some are for legacy reasons (multiple sites came together and we just never merged them).. some are for segregation of users (we don't want 'demo' users getting accounts on our main site).. and then there's some other reasons
In any case, we use JFBConnect on all 'sites', and while we use the same AppId, you could easily use different AppId's on each, allowing your Facebook Page to pull a Tab from each of those sites, if you wanted.
Again, hope that makes sense, but yes, we can walk you through it. Feel free to read our reviews on the JED concerning our support:
extensions.joomla.org/extensions/social-...egration/7215#action
Thanks,
Alex