I am trying violets and yellow sorrel as a living mulch, but carefully. If something is working as is, I'm leaving it alone.
Last year I interplanted beets and carrots and the beets did much better than the carrots. However, the carrots did much better there than they had planted in rows the previous year. So I guess they like company, just not too much. I plan to plant them in a bed again this year, but seperate from the beets. Possibly try letting some of the violets invade part of the bed, to see if they work better than beets, being a little lower growing. Not too many, though. The sorrel (relative of clover) gets a bit tall sometimes, about ten inches max, but its not as dense a plant as violets are. Those are going in the sunnier areas where plants like tomatoes and potatoes thrive. They are annual, while the violets are perennial. I'm using the
native sorrel for two reasons: a) its free and here, b) my dad freaks over the notion of letting clover grow, and so does my mom.
I am thinking of adding strawberries to my living mulch list because I found that they are very happy in my garden, while they sort of sulk elsewhere before producing (regularly, but not heavily.)
I do have plantain, thistles of three kinds, purslane, mallow,
bindweed, perennial sweet peas, and a few others in my garden, but they aren't welcome for various reasons. Bindweed for obvious reasons, thistles because of stickers and because the
ants import aphids for them, mallow and purslane because they literally take over and are a pain to pull out, sweet peas because they sprawl and smother everything but bindweed, quackgrass for obvious reasons, plantain because they attracted so many wasps last year that I couldn't harvest half my garden.
Its not like there aren't other things that blow in and grow. I either pull them out occasionally (like the catnip and tree seedlings) or enjoy them (like last year's petunias and this year's solo nasturtium). I also have plenty of volunteers every year: tomatoes, peas, beans, potatoes, onions, even a black walnut (which sadly died).
Also, while basil, lavender, and rosemary curl up and die in wet pots, they do fine as companion plants. I have lavender basically smothered by catmint that is determinedly growing out to the sun and looks quite healthy. Basil is said to improve tomato yields by 20% when planted about 10 inches from them. (I do know the one year I got peppers, they were smack dab up against a basil plant and both were very happy.) Not sure on rosemary, which tends to be grown with roses.