Ive found box squats to be an excellent tool for ME day also.
(Im joepalookas training partner... NOT the one who wanted him to compete single ply though, lol)
I think when joe and I were getting close to the 700lb range a box helped develop starting power AND it trained your muscles for depth. By that I mean that by having the box at parallel (or a bit below), you were teaching your muscles (by repetition) where to stop at.
The two box methods that I feel paid off were touch and go (just touch the box and ascend) and actually sitting on it and releasing your hips. When you reengage your hips you have to develop some helluva starting power to get that weight moving again!
On lighter weight I didnt notice box squats on ME day making too much difference, but for triples and singles it was nice.