Allow users to invite other users

I would like to run a friends-and-family instance that is slightly more open than an admin-approval-only instance. Specifically, I would like to allow existing users of the instance to invite other users.

Users can create single-use signup links from their settings that bypass the signup approval process. As an additional feature, it would be nice if the following worked

• Account request with admin approval is still possible as a parallel option
• I can limit the width and depth of the invite tree
• I can ban specific users from using the invite feature

I am taking inspiration from the invite option of closed mastodon servers and from private tracker websites.