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What about this: playing space is infinitive, new squares must be placed adjecent (diagonaly or orthogonaly) to other squares (but may become non-adjecent after moving); players can remove unoccuppied squares as well as put new squares; squares with opponent's pieces can be moved? Another suggestion (simple, but makes another game): any piece can leap over 'gaps'... And another one, not so simple: squares can make 0,5 step, in wich case it can be orthogonaly and diagonaly adjecent to 2 squares at same side (interesting that in such game rook's move sometimes can remind hexagonal rook's move)...