I think different species act differently, as well. I have I. germanica that needs dividing badly. I've done it twice since I got it 6 years ago. I posted it already but I'll do it again so you don't have to go looking. This was 3 rhizomes in 2009. I have given away lots and thrown away some.
The I. pallidas are increasing quickly, too. Both of these were single fans last Spring.