If each movement is broken into a piecemeal function, then a non-standard piece could be assembled, such as a piece that moves like a knight in 3 directions and a bishop northwest and southwest.
I have an overgrown dice pip renderer, so I made the rook "+", knight "L", bishop 4-gram, queen 8-gram, king octagon, and pawn a trapezoid (just to suggest movement direction).
https://vezquex.github.io/clock/chess/
There are flat chess pieces that have the traditional 2D symbols on top. Another question is whether anyone makes 3D knight pieces that are designed to lay flat on the board. Such pieces would fit a "Godfather" themed chess set rather well...