Dig it up and send it to me when it goes dormant this fall. I'll see if I can name it for you. My fee for the identification will be I get to keep the plant.

If there happens to be a peony specialist within driving distance, try them. Or maybe you could get them to help you via e-mail, your pictures are good enough that it might be possible to tell from them. Depends on how distinctive this particular type is, whether there are several that look just like this one or not.

'Kokamon' maybe?

milo, I do believe you've got it!!
THANK YOU!!

Sorry bboy, I guess Kokamon stays where it is ;)))

Here is a link that might be useful: More Kokamon

Kokamon sits-in Earline's gar-den
I-den-ti-fied is he-e-e
Laugh Kokamon
Laugh Kokamon
Laugh

I have Shimadaijin tree peony which looks sort of similar. The picture is two years old, as I cannot find last year's picture, but it is a very vigorously growing peony. It has tripled in size and the number of flowers by this year.
In real light both the flowers and the leaves are darker than in the picture.

Here is a link that might be useful: google search