Roses are a really classic combination with clematis, though pruning can be a bit fiddly.
I’ve grown a group 3 (late summer/autumn flowering) clematis to grow alongside my Montana because it flowers on new growth so literally just needs chopping down to the ground in the early spring and then you get all the green at the bottom each year.
In terms of shrubs, you’d need something that also likes nice moist, well-fertilised soil. What about a hydrangea? Or a weigela could be nice as long as you keep the size under control.
Avoid anything that likes acidic soil because you’d never be able to keep both plants happy.