Plugins Across Bungee

I have bungeecord set up on my servers. There's data that I need to be saved and accessible on the bungee level.

For example, let's say I have a log of a certain player's punishment record (Kicks, Bans, Mutes, Etc). I have 3 servers, and I would like for each time the player is kicked to be logged regardless of which server that player is on. And if a staff member checks that log, it would show every punishment across all 3 servers.

What would be the best way to do this? If I put the plugin in each server it just makes 3 copies. Could I access a plugin cross-server? If that's the case I could just save all of the data in 1 plugin and access it from the other servers. I don't need the code written for me, just a few pointers and help to get on the right track. Thanks!