You could always add in 10 sets of 3, sets across on the squat, once a week. It was enough for me to put some pounds on my squat, and I was a ways past beginner gains. Also, it's one workout, once a week. Reduce volume slightly elsewhere, maybe do the squat on a more technique oriented day to no screw with the pre-existing programming too much, or at least put them on a day where there will be a rest day the following day.
There's plenty of ways to do this effectively, just my suggestion.