As per this feature request, users of a private beta sites can invite fellow experts by entering their e-mail address.
I propose to extend this feature so that fellow experts can be invited either by e-mail address, or by Stack Exchange user id.
I'm not immediately opposed to the idea, but I think this would possibly open up folks being "spammed" with invitations. Since each invitation also includes an optional message, this could also be misused to contact people about unrelated stuff.
We have always been and continue to be very careful about making it possible to contact other users on our sites, so I hesitate to support this proposal outright.
While not completely foolproof, knowing someone's email implies a certain level of familiarity and personal acquaintance that being able to punch a number into a textbox doesn't.