Consider a chess variant where one can move all of one's pieces in one turn, instead of just one piece. This is motivated by realism: all soldiers in a real army can move at once, though some not as far as others. What other rules must change to yield a playable game?
In order to avoid the complexity of needing to know whether there was an exact moment (amidst all the movement) when a long ranged piece (rook, bishop, queen) had a open vista to move through the army, let's say pieces (or pawns) never block other friendly pieces moving though them. However, all pieces must occupy distinct squares at the end of a turn: no multiple occupancy.
Then, long ranged pieces probably become too powerful, so their range might need to be cut down. How much? Or make the board larger?
Enemy pieces, even if captured during a turn, can block movement of other pieces during that turn. In other words, captured pieces don't get removed until the very end of a turn.
A somewhat more complicated rule might be that stationary (they don't move at all during the turn) friendly pieces do block movement through them, but all moving pieces are assumed to be flying in air and other moving pieces can travel under or through them. So Pa2-a3 and Ra1xa7 in one turn remains possible.
Somewhat similar to Arimaa, and similarly vastly increasing the branching factor.
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