It won't grow under the maple, nothing will. If you're planting it outside of the maple's foliage line, it may just depend how far outside, how good your soil is or isn't, and what you plant, but the maple will continue to put out roots to some extent, and they're pretty shallow, so it's hard to say just what to do.

Can you use a combination of shrubs with lattice panels or fence in the areas you can't grow shrubs due to the maple? You might be able to grow vines up a lattice to give you some greenery if you plant the vines in pots raised off the ground slightly. (If you leave them on the ground the maple will send roots up through the pots' drainage holes, as I discovered in my own yard!)