We run WordPress Multi-site on two dedicated servers with an F5 load balancer in front of them. We use Wp Super Cache for caching. Tried W3 Total Cache to no avail (It’s probably a server setting on our end).
We use only a single database but I’m told it only appears as a single database it’s actually multiple ones.
Our biggest issue has been keeping static files (media uploads and wp-super-cache files) synced between the two servers. We use a program called Unison run every two minutes to sync changes between the two servers -> https://www.seas.upenn.edu/~bcpierce/unison//download/releases/stable/unison-manual.html
Our next step is integrating WordPress with the EdgeCast CDN for total caching (even the HTML, not just assets). This is feasible because our sites aren’t very dynamic. There are no comments and the pages, once published, are very rarely updated. Everytime a page is updated or deleted I make a call to the EdgeCast api to purge that URL from the cache ensuring the latest version will be available at the edge with no need for content creators to have to do extra steps.