It occured to me rather quickly that remaking the original icon is useless:



So, I decided to try random things until I did something that I thought was decent:



I think it resembles the original well enough. At first I tried to recapture the "multi-layer" part of the name but couldn't without making it look dumb, so I settled for some cheap bevel and decided to call it a bunch of buttons.

I also made a silly variation:



They even scale to 32x32 quite well!