I usually don't cut more than two layers, but more often I just cut one layer at a time. I feel I have more control.
I have a suction cup handle that I affix to my ruler when I cut and that seems to help the ruler not move so much. Another thing I use to make my rulers not slip so much is a pair of 8 pound (each) hand barbells, placed on the ruler when I cut. That much extra weight on the ruler makes it much more stable and less likely to move. It is more time consuming though to move the barbells each time I move the ruler and fabric.