What about other types of beans?
Green beans, yellow wax, purple?
Beans for drying, beans for eating fresh....lots of varieties out there.

Re. Purple Basil. I think it requires full sun to stay be deep purple. I have tried growing it in areas that get 4-5 hours sun per day and it won't turn deep purple. Actually is kinda streaked purple/green. I tried in full sun, more than six hours per day and it is a nice deep purple. I grow it mostly to allow it to flower. Bees love it.

If you are considering herbs, how about rosemary and thyme. They can take the heat, and four to five hours of sun while not optimal should work OK. A couple of our rosemary plants get sun in the afternoon only and grow nicely.

That' so weird, I posted a reply a couple of hours ago, but don't see it here! Anyway, I appolgize if it shows up later and I say the same thing twice. I was thinking chard might work for you, unless it's too hot for you to grow it over the summer. I had some that did well in a spot that was shaded mid-morning to about 3 and then shaded again about 5 to sunset. Also, sweet potato vine leaves sauteed taste fairly similar to spinach and they would likely grow there. Don't know if you could get them big enough to make nice tubers, though.

Cheers!

You know, my chard did pretty well in a simlar spot and survived last summer. I need a bigger spot as I only have a few chard plants right now, so I'll put some chard there. Not many greens will grow here in the heat, although we get almost sick of salads in the winter!
Opal, good to know on the purple basil, will still be worth it, along with some cinnamon and Thai, if just for the flowers. I like the lettuce leaf and genovese for most recipes.
I do need a thyme spot, love thyme, as well as marjoram and oregano. Have all the Rosemary we can use from a well established plant already.
I could probably start another parsley patch, too, my other patch survived last summer with some shade and reseeded itself. I do use a lot of flat leaf parsley.
I wonder if I can extend my green bean season into the summer with this spot, we have the shortest green bean season in Arizona, I can't seem to figure out how to do beans here.

Malabar spinach, okra, sweet potato, and watermelon.

I've been wanting to try malabar. I don't know if sweet potato needs more sun but I didn't get a single potato last year, just tons of leaves and small roots. Didn't care for the leaves much but only tried steamed and they may have been too large. Dogs, on the other hand, grazed in the SP patch daily!
Don't melons need full sun? Or close to it? I'm planning on a sunnier location for those.
I won't have this area ready for another month, possibly even two, as I have several other areas that take precedence. So, I may just try something that gets planted late summer for cool-season like brassicas and lettuces but I'd like to at least sow some cowpeas or soybeans to improve the soil, which is compacted clay right now. Do cowpeas and soybeans produce in less sun, at all?

I think 4 hours of sun will be too little for any crop other than some sort of leafy green. Especially since you say you tried sweet potatoes but got no tubers. But if you want to plant a legume just to make the soil better (not worry about if it produces), they can probably get that job done more or less.

Too bad the sweet potato leaf didn't work out for you! The way to harvest that (as I understand it) is to take the first few inches of growing tip to eat, otherwise you run into a surprisingly tough inner vein in the stem. I think I also tried snipping individual leaves off, but the older leaves had a stronger flavor that I did not like as much... I think; it's been since the summer before last since I tried them!

Cheers!