Automatically add users to WP Multisite sub-site based on role

So, I have a request for something I’ve not seen elsewhere. I look after a community website for a gaming server, and I wrote a system on that server that sets in game permissions for staff members based on their wordpress role. We are now moving all staff resources to a separate subdomain on multisite. I’ve got most things working how I want them to, but I have run into an issue.

We manually set staff members to the appropriate secondary role, but we now need that to not only sync to the other site (which I can already do with an existing plugin I believe), we need them to be dynamically added to the sites user list, and vice versa when they cease being a member of staff.

That’s my problem, and frankly I’m not sure how I can do this. If someone could explain something in PHP I can implement (I’m not proficient, but I can use it!), or even an existing plugin I would be very grateful.

Thanks,

Ben