Edit custom WordPress plugin to allow cross-site DB Access

I have a custom wordpress plugin for storing and searching courses. The courses are stored in the wordpress DB. I need to customise the plugin so that i can add it to a second website but still look back to the database on the first website.

Website 1 - Add locations, classes, and class to course relationships
Website 2 - Install customised version of the plugin which reads database to display and search courses in website 1 DB
Website 3,4,5 - needs to be extendable so i can add to multiple websites looking back to main website 1 in the future