It depends in part on the weight of your finished framing. There are several different modes of attachment other than screw eyes. Lowes, Home Depot, Michaels, Aaron Brothers all have sections with a variety. But, even they will leave marks when stacking. And the wire itself could leave scratches.
When stacking the best approach is to cut a piece of mat board to the size of the larger frame and put it between the frames. You could use any firm cardboard if doing it for just a short move. But, for longer storage or definitely if there is any possibility of the art touching the separator be sure to use an acid free mat board.
Gary
Professional Framer (retired!)