This is probably never something I would do as in my situation I feel I would spend more total time at the gym and gym related activities if I lifted twice a day. And my personality type prefers to get it all done in one shot and move on. However, your post has peaked my interest.
Maybe a way to further improve recovery would be to do a different supplemental lift than a main lift. For example do 5x5/3/1 in the morning for Bench and then in the afternoon simply work up to a Widowmaker set for the Squat. That would be a particularly quick training session in the afternoon. On the other hand does a Widowmaker lose some of the merits of doing it if you do not do it in a fatigued state after the squat main work?
The above is just one example, but those are the kinds of questions I would be asking when building my programming for training 2 times a day.