Vegetables that don't need a lot of direct sunlight (lots of light though)?

There is about 15ft x 15ft behind my shed that doesn't get a lot of direct sunlight ... but it does get a ton of daylight though. The shed/garage blocks most of the direct sun and as a result, this area is slightly shadowy. I was wondering if there are any mid-summer vegetables I could grow in this area that doesn't need a lot of direct sunlight and would do well with daylight. I already have a lot of tomatoes, cubers, marrows, potatoes, and herbs in the sunny areas. I live in NE usa