You cannot simply modify wp-config.php to point at multiple databases. If you need those specific requirements and no existing plugin can do that, then you will have to write your own plugin or hire someone to do it for you.
You will have to think exactly what you want your plugin to do besides "have a separate database for each site". For example what happens if someone creates a new site... how does a new database get created for that site.
Will your WP system really be that big to require multiple databases vs one large database server? Our system is fairly large and we havent come to that point yet (multiple db): 300+ sites, 3000+ tables, 4GB database. We are still on one database server which is mostly idle.