I would think it too much shade for squash - if I'm picturing it correctly. But take advantage of that shade and plant something that not only has similar nutrient needs but will benefit from that shade. Maybe lettuce, spinach or other leafy greens that normally wouldn't grow later in the season without lots of shade and cooler soil.

Shady places like that also make a good seedling nursery for any flats you have going of fall plantings. Protects them and hardens them off at the same time so they are ready to be planted as the room opens up for them in the fall.

Dave

Do you have a photo of your trellis in place to share? I agree with what digdirt said, in general. I might try growing peas there until the tomatoes grew large.... they grow in different parts of the year for me, so they could use the same space/trellis with some slight overlap in growing seasons.....by the time the tomato was enjoying the summer heat, the pea would die down.

An a-frame suggests 2 trellises leaning or connected at the apex. If it's running N to S, why not separate the two frames and secure them perpendicular to ground? (regular vertical frames). That way, you get the same trellised area for your tomatoes, while opening the area between the trellises to sun and perhaps a healthy summer squash play. Else, try a single summer squash plant at the southernmost point between the a-frame and the rest of the area in greens. Just my 2 cents.