Wordpress MultiSite - Under construction question


I have a WP Multisite installation with three sites (subdomains):

example.com (wordpress)
sub.example.com (buddypress)
sub2.example.com (wordpress)

I use an "Under Construction plugin" for the "example.com" and for "sub2.example.com"

Buddypress is free to visit. The problem is that when a participant of the buddypress community is logged in can visit the other two sites, bypassing the "Under Construction" plugin.

P.S. I tired many under constructions plugins but no luck.