Multisite Maintenance Mode solves the problem of site users making content/database changes while performing maintenance on large multisite networks. It works by directing every user (except network admins) to their homepage when they attempt to log in. A message is displayed in the admin bar to direct them on where to find more information. Anonymous users can still view the site normally.
Unzip and upload to wp-content/plugins
Network activate the plugin
Go to Network Settings -> Multisite Maintenance Mode