Start. This started out as an attempt to emulate the Eight Queens problem in Chess.
As a two-player game you would each in turn place a pawn on the board in such a way that no two, of either colour, would be en prise to each other, and the winner is the last to be able to make a legitimate placement. The obvious approach would be to place them all on blue squares, as shown here, but in this case it's unlikely that more than 11 of the pawns could be so placed.
To make it easier, you could merely insist that no pawn should be en prise to one of the opposite colour.
To see whether this would be workable you can treat it as a solitaire and seek to place
as many pawns on the board as possible in accordance with this requirement. I've tried
it several times and never managed to place more than 12 pawns successfully. Can you do better?
A pawn moves from red like a rook, from yellow like a bishop, from green like a knight, from blue like a king. It can move any distance up to but not beyond the next square of the colour it started from. It may not pass over or land on another pawn except to capture one of the opponent's. (This is a game of placement only, not movement, but the rules of movement dictate the legitimacy of the placements.)