How many times will an anenome split?

A couple of weeks ago, after being out of town for 2 weeks, I was
pleasantly surprised to find that my rose anenome had split twice
(from one to three). Since my tank has limited high-light areas
necessary for anenomes, I ended up trading one into the LFS for
credit. Lo an behold, after returning home from a week trip, I find
that it has split again. That makes three splits within about a month
period. Has anyone else had this experience? I am very glad that the
anenome is happy enough to be reproducing so much, but I am curious
now about how much, and for how long I can expect this to occur.