The best source of information on reblooming iris is the Reblooming Iris Society, a section of the American Iris Society. It gives you lists of iris to grow in your area. The site has other tips as well as information on reblooming beardless iris such as Siberians. Always look for names of iris that grow close to your temperate zone. The number of varieties of reblooming iris are increasing for Minnesota zones 4a and 4b.
There are a number of things one can do to increase fall rebloom besides selecting the right varieties.
1. Plant and grow more than one. Two clumps will increase your chances.
2. Grow iris in full sun. This seems really important.
3. Plant in the best possible soil. Rebloomers are hard to rot so a little more nitrogen and water will help.
4. After the spring bloom, cut old stalks right away and make sure the plant does not go dormant by fertilizing and watering. Watering is the most important in hot weather.
5. I do not replant reblooming iris as much as others. If you have two clumps, replant one so you can enjoy the other. If you see the plant not doing well, by all means replant.
6. Each fall the frost will get some stalks before they bloom. If you cover, like with tall plastic rose cones, it can get you a week or more of bloom. Many stalks did not bloom this year because of a late spring bloom and a resulting late fall bloom.
I do not still grow all of the bearded iris listed. You may fair better than I on some of these:
Again and Again. TB. yellow. Blooms half of the time (fall)
Autumn Jester SDB. purple. First year in the garden. Bloomed.
Baby Blessed SDB. yellow. About half the time. Has a better reputation.
Blueberry Tart SDB. blue shades. First year in garden. Bloomed.
Champagne Elegance TB. light peach. Infrequently in August.
Champagne Encore IB. shades of peach. Regular fall bloom.
Cheyenne Capers TB. a red and yellow plicata. Seldom but nice.
Corn Harvest TB. yellow. Occasionally.
Double Shot TB. white and purple stripes. Infrequent.
Eternal Summer IB. violet. First year in garden. Bloomed.
Feedback TB. dark violet. Infrequent.
Forever Blue SDB. blue. First year in garden. Bloomed.
Forever Violet MDB. violet. First year in garden. Bloomed.
Harvest of Memories TB. yellow. Seldom.
Immortality TB. white. Half the time.
I Do TB. white. Half the time.
Juiced Up SDB. lt orange/yellow. First year in garden. Bloomed.
Low Ho Silver IB. silvery white. Often.
Midsummer Night's Dream IB. dark purple. Rarely blooms.
Over and Over TB. blue and white plicata. A little over half the time.
Queen Dorothy TB. purple and white plicata. Regular fall bloom.
Rosalie Figgey TB. purple. Regular fall bloom.
Total Recall TB. two-toned violet. Infrequent.
Unbelievable Love TB. blue/violet. The most reliable rebloomer I have.
Velvet Toy. Dwarf species cross. purple. Some of the time. May be lost.
Zurich TB. white. Regular fall bloom.
(Note from MH: I planted SDBs Forever Blue and Autumn Jester in 2012. Both bloomed in spring 2013 and again in fall 2013, and since I didn't know they could rebloom, I gave them no special treatment.)