Found this for you. I have some clumps I have to transplant myself.

"Cut the peony stems near ground level in September. Then carefully dig around and under each plant. Try to retain as much of the root system as possible. Promptly plant the peony in a sunny, well-drained site.

Division of large peony clumps requires a few additional steps. After digging up the plant, gently shake the clump to remove loose soil from the root system. Divide the clump into sections, making sure each division has at least 3 to 5 eyes (buds) and a good portion of the root system.

Peonies grow best in full sun and well-drained soils. Dig a hole large enough for the entire root system. Place the peony plant in the hole so the eyes are 1 to 2 inches below the soil surface. (Peonies planted deeper than 2 inches often fail to bloom satisfactorily.) Fill the hole with soil, firming the soil as you backfill, then water thoroughly. Space plants about 3 to 4 feet apart. Apply a 2 to 4 inch layer of mulch in late fall. Straw is an excellent mulch. Mulching will prevent repeated freezing and thawing of the soil that could damage the plants. Remove the mulch in early spring before growth begins. Transplanted peonies will not bloom well the first spring. They should be back to full flower production by the third or fourth year."

peonies do not like to be moved, but if done right will give you no trouble at all. DO NOT move them now or you will certainly not have any blooms this year and maybe next year. I tried this. I dug the largest root ball I could, took as much dirt as possible and the huge plant refused to bloom or even grow well. This is a plant that was commonly covered in flowers. September is the best time, and still be gentle with them.

Thanks for all the info! I did try moving one (OF MANY) and it was a disaster. I'll wait to do more if at all, in September.

I dug a Festiva Maxima Peony two years ago in the spring. It was a large established plant that flowered profusely. I had to move it, or lose it. I dug around it and wound up breaking the crown into sections by accident. It was in bud at the time I had to move it. I planted the three sections..two large ones, and one small one. The transplants all survived, although the buds never grew larger or flowered that year. The following spring, they grew again, but no buds/flowers. This spring I see them starting to grow again. I am hopeful to have them flowering this season. I usually plant my peonies in the early fall and they have, for the most part, flowered the following spring. I do not know if the fact that I moved it in the spring, or that it was divided into smaller plants was the issue for it not flowering, but I have three now, where I would have lost it completely had I not moved it. Good luck with yours.