An interesting chess variant is Free Castling Rule.
The Dictionary of Modern Chess indicates that this was played in 17th Century Rome.
Here white may castle Queenside and black may castle Kingside.
This is one possible way white and black may castle under these rules.
The most popular Kingside castle in Free Castling involves moving the king to the h-file and the rook to the f-file.
Shown is yet another way white and black may castle.
There are many more possibilities.
Dictionary of Modern Chess, Byrne J Horton 1959.
Diagrams were made with Chess Captor.