Invitation-only events?

I would love to use Events+ to manage invite-only events (all invitees will already have WP accounts).
Ideally, I'd like to be able to send invites to particular users, and only if they are invited will they see the RSVP options.
To really make my day, I'd like to be able to show or hide events, so some are purely invite-only (no one else sees that they exist), and some are publicly viewable, with a "request and invite" button.
Any chance of doing any of that?