Fine as long as you leave most of the foliage. However as the peonies expand and grow it will not be posible to do do in the future. You will need to move one or the other of the plantings for both to be seen at their glory.

Thank you, Maifleur. I tried to respond to you last week but the site was not functioning properly. I had a hunch that would be your answer but was hoping it would not be. My neighbour came over today with some rather long stakes (I had the shorter round wire supports) and tied them up quite high so the shading tends to be reduced. In the fall will be a good time to re-locate my other plants and let the peonies be the 'stars' of my garden. They are just so full of buds just waiting to pop open. Do you ever remove buds to promote fewer, but larger, blooms? Just wondering.

I don't but it would depend on what you want. By removing the buds the main bloom will be fuller. By leaving you will have a longer blooming time.

If I wanted for a special event I would probably remove the buds but personally I like the longer bloom time. Additionally if you were going to breed peonies sometimes the side buds on doubles will have pistles and stamens where the main bud does not.