Is it possible to put plants around the base of a tree?

I have two crab apple trees with beautiful blooms in my yard and their branches are touching. My father would like plants around the base of the tree. Now I know that is tricky because of root competition and the high amount of shade. We are in zone 6a. Any suggestions for what could be planted there? I’ve had the idea of planting native perennials, which would also help the local ecosystem and the garden. Any ideas for that?