Is it possible to configure Account Activation Mode for both Admin Approval AND Invitation?

The account activation mode for our site (10.0.3) is configured for Admin Approval in Authentication Options > Account Activation Mode. One of our key stakeholder groups would like to bypass the manual step of admin approval by allowing account approval to those invited to join a group. It appears this could be accomplished through setting account activation to Invitation Only. We would still like administrators to approve those seeking to join our community without an invitation.

Questions:

  1. Would lose new user sign-up and admin approval if we switched to invite only?
  2. Is there a way to allow both admin approval and invitation only modes?
  3. If we lose new user sign-up in invitation only mode, how could we direct potential new users to receive an invitation?

Thanks for any help that might be available...