When the plant puts out more buds that it can support sometimes that happens. It requires a lot of energy to take the buds all the way to bloom. Fertilizing after the blooms are done and before the roots go completely dormant and then again in the spring can help. It isn't going to hurt your peony, though, if you're worried about that. If it still has buds that you feel can make it to bloom I'd pinch out those that haven't increased so the plant can concentrate it's energy on the viable ones.

Thanks