OSM Maintenance will allow you to put your WordPress site in Maintenance Mode so you can upgrade files without fear of bringing your site down.
It works by blocking all IP Addresses except for a specific whitelist that you set.
Does this plugin work to set an entire Multisite into Maintenance Mode?
Yes! When you network activate the plugin, all the sites in that network will go into Maintenace Mode.
How do I add IP Addresses to all the sites in my network without going through each individually?
Go to the Network Admin Dashboard -> OSM Maitenance page. From there any IP Address you had or remove will overwrite the individual sites’ settings.
First version of the plugin