If the ground is moist, there are some interesting perennials to use such as amsonia hubrechtii and the sedge, carex testacea. The three provide a nice fall foliage color combo with the itea turning red, the amsonia yellow and the sedge orange. However, that's not a flowering group if you want blooms. The amsonia has tiny little blue flowers in spring. If you want more blooms in moist soil, daylilies (deer will eat), canna, Japanese or Siberian iris, or bee balm will work.

Little Henry blooms in late spring here (zone 7), so I consider it a nice green backdrop during the summer. Which gives a lot of possibilities with perennials. What colors do you like?

Since Little Henry has small oval leaves, I would look for a frilly and a spikey plant to use to compliment.

I can only speak to zone 7 plants, so check to see if these work in your zone:

If you like blue/purple, nepeta 'Walker's Low' blooms from spring until frost. The flowers are on soft spikes. Bees love it. It can be divided easily in the spring for more plants. It's a nice tall edging plant, too. I cut it back in fall or early spring and then cut it again after the first bloom to get more blooms. I use Black & Decker cordless HedgeHog trimmer to make it easy.

In this photo, nepeta 'Six Hills Giant' (taller than Walkers Low) is behind Spanish Lavender.

In this photo, I have purple sage (foliage) and aster frikartii 'Monch'. Again, these are for dry soil. They also work well with the lavender, nepeta and Little Henry.

I hope this helps.
Cameron

Here's of my Itea just starting to bloom:

Miscanthus Little Zebra is one of my favorite ornamentals for a less than 3' ornamental grass:

Siberian and Japanese Iris also work with Little Henry. I have these all along my garden paths in the moist areas near the itea.

Cameron