It is called double socketed blooms. I only have one that consistently has 3 double sockets. Love 'em.

You're right. A rebloomer usually sends up a new stalk several months later (in the right conditions). But there are some that do it more quickly. Often labeled everbloomers. Sorry I don't have names. The only one I remember that kept producing new stalks was 'Amour'. A pastel peachy-pink with white falls edged peachy-pink. Don't know if it repeated in the fall.

Yours is wonderful! Edith Wolford has those colors but is usually much taller.

Thank you so much for your help! This is an established yard with tons of plants, but they are new to me - just moved here 1 year ago. I've never heard of double socketed blooms and truly appreciate the information. I'll look up Edith Wolford - most of the plants here were uncared for and are just beginning to emerge from what was a weedy mess. Perhaps this iris has not been able to reach it's full height - with a little more care it may become more robust in the following years. Amour sounds truly lovely - I'll see if I can find that one to add to the beds.
Thanks again - you rock!