Caesar's Brother is a tenacious ground gripper by the ten year mark - the "hole" in the middle is generally old dried rhizome stock. Once big chunks of it are out of the ground, a pruning saw works fairly well to get transplanting sized pieces - it just laughed at various types of knives. The white counterpart, Snow Queen, doesn't seem to enlarge on that scale.

In general, the recommended time to divide/transplant spring blooming perennials is in fall -- that gives them sufficient time to settle in and re-establish before bloom season. Having said that, I've moved/divided Sibes successfully at all times of the year :-) In mild winter climates, you can get away with a much wider range of routine gardening activities......

Siberians are tough as nails. Although conventional wisdom usually dictates fall, I've never had a failure doing it any time the need to arose. Been an unusually cold and wet spring, first days of summer here, too, and the Siberians are still blooming. I'd at least wait until the blooming's over if that's the case with yours, too... and cut down the stalks and trim back the foliage a bit to make digging up, handling, and dividing easier. Be sure to have a sharp shovel - I've occasionaly had to separate a big clump of them with a pruning saw. Prepare their new spot in advance and water them in.

I divide mine in fall. The "rule of thumb" is if it blooms before midsummer (end of June), then divide in fall. If it blooms after midsummer or into fall, you can divide in spring. This allows for sufficient re-establishment of the root system before the flowering cycle and minimizes disruption to the bloom cycle.