Well, I have
chickens under the tree too, so the collards grow up out of beak's reach and they keep the base pretty weed-free.
The plum is rather near to some raspberries, but they are not exactly under the tree. I have quite a bit of catnip too, which is
medicinal (kills a cold) and not bothered by the
chickens.
So I imaging you could try some oregano or thyme, or other herbs. I also like to sow bell beans and daikon just all over, so those things are there too. Bell beans are mostly for the green matter - you could grow the culinary fava type instead, the daikon is a good soil builder, mineral accumulator, and also edible (tops and
roots). I let most of them go to seed and then rot.
I always grow some sort of winter squash which will reach out in many directions, and sometimes the stems make their way under the plum. You could plant squash at the base of the plum in the spring, and it would create a nice shade for the base.