I want hostage chess. It is the only variant which can be played with a normal chess set. Even chess can require upto sixteen extra pieces for promoted pawns. Hostage chess is also somewhat similar to crazy house. The difference is that your own pieces are dropped into the board and not your opponent's that you have captured with colour changed. www.hostagechess.com/ is a website dedicated to the game. You can also find an excellent book on the variant and a playing program downloadable from that site for free. I'm not associated with that site in any way. I just find this variant extremely interesting.
I think this will never happen on lichess.org but all ingredients are there so I started github.com/gbtami/pychess-variants It's in very early stages and full of bugs, but you can try it at pychess-variants.herokuapp.com/ It starts slowly because Heroku send it to sleep mode after some inactivity. You can play with Random-Mover BOT or with human if you can grab some partner there :) You can choose westernized pieces for Xiangqi and for Shogi clicking on the upper right corner cog wheel icon.