You can have fences visible only when hovered over (which I like better than having to have a master icon in each region). But you can't have one fence on top of another one.
Actually, you can put them on top, but only one is on top, so when you hover over an icon on the visible layer beneath, the top layer takes over and you can't access the overlaid icons.
There's probably a way to select a fence without a master icon....
I really prefer my desktop completely free of icons most of the time.