Fungia can be fragged...
I haven't posted here in a long time, but a couple of years ago I had a thread where I fragged a fungia. I used a dremmel with a diamond wheel to cut it into 9 pieces like a tic-tac-toe board. or a #hashtag. They each grew a new mouth, and quickly started to round out as they grew. I had a couple of them left when I finally broke my tank down.
It looks like I can't find my old thread on here, but I also started a thread about it on NR.com
http://www.nano-reef.com/topic/198351-fragging-a-fungia/
cheers!
dsoz