I use an awesome pair of kitchen scissors to snip the Live Rock around Ricordea mushrooms into a small chip, attempting to leave the foot's grip on the rock chip undamaged.
Then, I use superglue (cyanacrolate) gel to glue the CHIP to whatever rock I want to, holding the glued rock underwater while it cures for about 15 seconds.
You can use this to combine different types of mushrooms on the same rock, or to make Rainbow Ricordea rocks.
You can also combine other corals, of course.
The main thing is not to let glue get on the shrooms- they hate it and slime away from glue.
You can also slice many types into small pieces- but they take awhile to attach and usually get lost in the current and die. Bridal Veil can hold them in place for this, but I like just moving the chip they already have a healthy footing on.
I agree that some shrooms can turn into plagues- usually the little striped, spotted, or green discosomas that just take the reef over with little SPS-stinging babies.
I love Rics, though!