I have read on some of the 'how to divide peonies' instructions put out by major growers where they say too many eyes can hinder the development of the replanted peony. Seems there is a correlation between the size of the roots and the number of eyes which they can support during their first few years. 3 to 5 eyes seems to be the normal standard for quality peonies. Of course, larger root clumps should support more eyes.