I fiddled with intercepting and reverse-engineering it before the shutdown, probably still got the packet dumps somewhere. It's one big XML file, so if you can get around the SSL restrictions (we still don't have a great way of doing this) it'd be easy enough to start making custom Miis and posts and games and whatever show up on WaraWara Plaza.
Here's an example of that kind of customisation in Splatoon:
The Big Issue with this kind of mod is that either the server needs to get by without knowing what your username is (difficult when making posts) or we need an unofficial NNID login server - while such a server was in development back when Miiverse went (I haven't checked on it since), since you were logging in with homebrew and not Nintendo, all Nintendo's online features think you aren't logged in. That means no online multiplayer, no eShop, nothing; and making it work would require homebrew replacements for all these services. Since most of the Miiverse-heavy games (Splatoon, Smash etc) also have a multiplayer focus, it didn't really make sense to break online like that.