In that sort of a situation, you wouldn't use a seperate button for each one -- you'd have some way in the login id to specify if it were a remote id. Most rent-a-POPs use this. (The companies that rent out modem banks, so that other ISPs can claim to have 'nationwide' coverage).

If you have to log in as user@domain or user/domain you've probably gone through one of these -- when the radius server that you're authenticating off of see the domain, it checks to see if it's a domain that it knows about, and if it is, it uses whatever authentication check is necessary to authenticate in that domain.

So, I might log in as ONEIROS@PAUSE or oneiros@perl.org or jhourcle/perlmonks or whatever_my_local_userid_is_without_a_domain or however the system handled things.

You're right, however, in that there is n*(n-1) complexity for the system administrator, as each of the n sysadmins needs to know how to authenticate to n-1 other systems -- but it doesn't require a seperate login blank for each one, or a button for each one.