Generally, you need to pull as much thick mash as you need to hit the next rest temperature. Brewing software (or great math skills!) is extremely helpful for this.
If you pull too much, you can overshoot your temperature when you put it back in the mash. If you don't pull enough, you can miss your temperature also.
I don't think I've EVER done a 13 quart decoction, though! That's a lot.
Normally, if I'm doing a protein rest, I'll do it on the high end (like 131 degrees) and then almost immediately pull the first decoction as I don't want to stay long at protein rest temps (I use well-modified malt). Then I hit the first saccrification rest, stay there for a time (30 mins), pull the next decoction for the second saccrification rest, and for the last decoction I pull thin wort instead of a thick mash for the decoction to mash out.
Normally, the amounts are 5-8 quarts or less, in a 5 gallon batch.