Answer: As you've seen, disbudding, or removing all but one flower per stem, results in fabulously large flowers! However, even if you didn't disbud, chances are you'd have problems with the plants toppling over under the weight of the flowers. However, overfertilizing can contribute to overly succulent, and therefore weak, growth.
There are several methods of supporting the flowers. Whichever means you select, it is a good idea to set it up before the peonies reach their full height. One is to use the purpose-built traditional peony rings which are short enough to "disappear" as the plants grow up through them and broad enough to encompass the entire plant.
Another method is to set several stakes in a ring around the perimeter of the plant and then wrap string spider web style around and through the stakes; again the plant will grow up and through the support.
Yet another method is to set a section of wire mesh such as chicken wire on the ground and allow the plants to grow up through that, raising it with them as they grow taller.
These will all support the plants evenly and gently and be nearly invisible. Finally, if all else fails or it is too late for the early support methods, simply tie a few lengths of string around the perimeter of the plant. This will enable it to hold itself up...but also makes it look like a trussed chicken.
Enjoy your peonies!
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