Create anti-perpetual check and anti-stalemate mode!

Basically, the stalemates, perpetual checks, and other useless cycles can be alleviated nearly 100% without changing the game much and while it modifies the rules of the ephemeral chess, it does not change the game any except at the end game by modify the possible games.

1. If the king only has pawns left to protect it, it can use the corner squares as teleportation to the opposite corner and counts as a move.

This prevents easy stalemates.

2. The king can optionally move 2 spaces if he has made the same move cycle 3 times in a row(repeated the same set of moves, whatever length, 3 times).

The second move is meant to reduce the perpetual check outcomes to virtually 0. Essentially the players king can surely get out of the perpetual check in most cases because having an extra move allows him to reposition himself in a much greater number of situations.

This moved can be saved up and used any time after it is "activated"... only once though.

Together these extended rule do not effect most games so chess will be chess. But they turn most end games that end rather boring in to something that has a bit more of a challenge

Any other rules could be added for the end game that helps make the king stronger so he can break the perpetual check.

e.g., what if the king has the ability to knock back or reset any piece that has put him in to check if that same piece just put him in check. This too would reduce perpetual check end games.

Big issue with even just the general concept is that stalemates and perpetual checks are one of the only remaining options a player in a losing position has left. If the winning player missteps, the losing player can take the opportunity to salvage a draw out of it. Without the possibility of a stalemate or perpetual check to save the game, more resignations are bound to happen even earlier in the game.

Also, you're about 2,000 years too late to add a rule. :P

Then K+P vs K is a win
The Philidors position isn't a draw
This just slaughters all endgame theory ever

Better yet, allow any piece to "jump" away from being captured and land on any square of it's choosing. Chess would be so much more fun !