Chess can straightforwardly be extended to a 9 by 9 board: each side gets two queens. If we use the orthodox chess-inspired initial position RNBQKQBNR, then all the bishops have the same color, which might not be such a bad thing: avoid draws of opposite colored bishops. The bishops get to wander on the majority color: 41 out of 81 squares.
This method of extension has the advantage of preserving most old chess wisdom (in contrast to introducing different piece types like Capablanca chess or shogi) but creating a 27% larger game.
A Chess960-style shuffle preserving bishops all on the majority color yields 2100 possible initial setups. If we just want to avoid both bishops on the minority color, then 6300.
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