Insert snippets globally across entire multi-site network

My team manages a multi-site network of 100+ blogs, most of which are maintained by (very) non-technical users. Most of the changes we make are implemented globally across the entire network, NOT on a specific blog.

From the testing I’ve done in our test environment, it looks like this plugin only works at the individual site level, not the network level. Is there a way to run this plugin at the network level so I can add a snippet once have the change appear on every site.