If you want a 4-player Mah Jong game (never seen Shanghai or mini S.; no clue what they're like) you can try the one at
www.ninedragons.com They have a fully-playable demo version, plus a rules guide on the site. The rules all won't necessarily apply to the Neo·Geo versions, since Mah Jong rules can vary slightly literally everywhere the game is played.
The only other 4-player one I've come across was a (seemingly) very famous hentai anime one, and Visco actually made one this year or last, but I would have to re-check what it was like, as well as platform.
Come to think of it, all the Neo Mah Jong games are either related to sex, or in the case of Minasan, dirty humour and actions (you'd have to see/know about the show it was based on, which is supposedly the same programme that served as the influence of the Ping Pong Club anime, if that tells you anything).