It happens. We try to work with everyone and then the shoot either runs longer, traffic, and everything else happens. The next assignment is furious! I actually got burned on this two times and then decided that I was never going to book two assignments in a day. Not just because my look was not going to be as fresh as it was at 6 am but, that I would have someone waiting.
The courtesy of this is to only book one shoot or to leave enough time to have ample buffer for the next assignment. And also let the first assignment know when you need to leave.
Communication is everything. You need to be honest with yourself and with each team on whether you can actually pull off several shoots in a day. And still look amazing. Also to look rested. Be professional in this. If it is not feasible, then move around the schedule so that it is. They will thank you for it!!