I'm rewatching Saw 3, and it would be interesting to expand the Pig's powers in some ways.

1) Give the Pig an alternate head trap. You could shift between them like you switch the Clown's chemical bottles. The Shotgun Necklace trap would be an interesting one. In the movie the character with it on has it set to trigger if Jigsaw dies. What if this one triggered if another survivor died? Obviously you can go to a puzzle cage to remove them and not worry, and it won't have a timer, but it will kill you if another survivor dies through a More or on a hook. It would be a choice of self preservation and removing the trap vs altruism and focusing on saving characters in place of you.

2) You could alternatively give the pig a syringe to stab someone with that slows their movement down unless they acquire a cure from a puzzle cage. This reminds me of the second film where everyone in the house is dying from a poison which effects them negatively, and they had to put themselves into a dangerous situation to find a cure.

3) Make it so that when you interact with a puzzle box that you are injured after. The point of saw is that you survive if you are willing to harm yourself and push through the pain. Maybe you can either acquire a PERMANENT status effect for the rest of the game when you solve one, or maybe it can always decrease your health state by one level if you interact with it, successful or not?

I feel the pig is fun but not as strong as other killers and these might be potential good suggestions to improve their ranking in the game.