I run a private Discourse for our organization and currently restrict users to only those with a company email address. Now I have need to add a few users with non-company email address but still need to keep the site private. Is it possible to open up user registration to all email domains but limit only to those that I invite?
Yes, enabling the
invite only site setting should accomplish what you are looking for. For details about sending invites, see How to send, configure, and accept Discourse invitation emails.