Someone correctly pointed out that on DE days, the box is at or below parallel to reinforce depth and greasing the groove so to speak. That does not mean a box cannot be used for other purposes, much the same as multiple boards. I would not however, use a higher box on DE days because you want to work dynamically thru the full ROM.
Yes, you can absolutely fail at ANY point above the hole in a max effort squat. I see some people here have never spotted at a PL meet or otherwise attended one. A higher box can be used to address specific weaknesses (although there are probably other means either equal to or superior to do the same) or, it can be used to overload and get a feel for some heavier weights you otherwise cannot do full ROM.
The key is to know WHY you are using whatever methodology you choose. There is really no benefit to change box sizes just to “change things up”. If you’re training for PL, you want to stay with a box at legal depth. You’re going to get that answer b/c the popularity of the box squat (its recent reemergence) came from a decidely PL background gym (WS). If you want to “change things up”, you want to add bands, chains, different bars, wave load your DE work, your ME work, etc. But if you’re training for PL, and you box squat, no need to go higher than legal on DE day.
As for addressing weaknesses by means other than a higher box, there are a host of special exercises that will fit assuming you correctly diagnose your weakness.
So, after that long winded (sorry) response, yes, you can raise the box, but do so with the correct purpose for your training goals. PL’s DO take higher box squats on ME day.