Is there a full-automatic burst shotgun?

Shotguns are nice because they make big holes on their targets. Burst rifles are also nice because they make a lot of holes really fast with only one trigger pull. WHAT IF We add those two destructive features together to get a burst-action shot gun? Could that actually work and be efficient, making a lot of big holes really fast?

Atchisson Assault Shotgun

Not a production model but still impressive; belt fed auto-shotgun.
It is not mine and I call it BASH. Belt-fed Auto Shotgun; Homebuilt

https://www.youtube.com/watch?v=iX7vwivR6cE

http://en.wikipedia.org/wiki/Automatic_shotgun

several models listed

They’d probably pound the hell out of your shoulder.

https://www.youtube.com/watch?v=WOoUVeyaY_8

http://en.m.wikipedia.org/wiki/Heckler_%26_Koch_HK_CAWS

Recoil and insufficient range outweigh perceived benefits of target saturation.

The AA-12 uses a gas system and recoil spring to lower the recoil to 11% of what you would feel with a typical 12 Guage shot.