How to make a general forum with closed sections for individual sites in the WPMU network?

Question

Social media

It is necessary that in a multi-site network with a sub-domain option and with the attachment of separate domains, there should be a forum common to the entire network, located on a separate subdomain (for example, forum.example.com or forumdomain.com), but each network site (site1.example.com, site2.example.com...) would have its private sections (e.g. forum.example.com/site1, forum.example.com/site2, forumdomain.com/site3...), which can be seen by joining the site's community networks.