It says
"To my knowledge (please prove me wrong!) it's impossible to get full rigidity in the basic rules system already described"
Someone took this challenge here:
https://groups.google.com/forum/#!searchin/puzzlescript/rigidity/puzzlescript/LvKcPQ-KI18/e0DbpplZoAkJ
but it still doesn't work in some cases.
Here is my attempt at making rigidity:
http://www.puzzlescript.net/play.html?p=45a14244d3d80fc288adba2b5b8bf42b
This works even if there are multiple players, and also allows for an arbitrarily large amount of boxes without adding any more rules.
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Fixed (I think?):
http://www.puzzlescript.net/play.html?p=a0207869ba37ddcc3593bb3b9844b38c
Surprisingly, I didn't actually change the rules at all! Only the objects and legend sections are different.
It's an interesting question, because I don't think it's possible to fix that problem even theoretically.
What should be the expected outcome in the scenario you gave? Should the up-goer push one piece, and then the left-goer push the other? Should the left goer push both pieces? Should the piece being pushed by both move in both directions? Should no piece move at all? It seems to me like there's no obvious outcome.
You could have all players move separately, but it's also fine when players moving in the same direction move together, so here's a fix in which that happens and all directions go one after another (Like in the game Perfect Paths).
http://www.puzzlescript.net/play.html?p=b5b9c318e4a8412bfb08c321052d958c