Thanks for the information.
Currently plugin caches available WordPress admin back-end menu when you open “User Role Editor” page under user with “Administrator” role. In your case single site “Administrator” has limited access and thus his cached menu is not full. I need to cache admin menu for network superadmin possibly or find another way to get from WordPress the information about full admin menu.
It seems that I need to run additional tests of “Block admin menu” module against WordPress multisite and make some updates. I will return to you with the new information as I resolve the problem.