Not trying to be negative, but I believe you will have a difficult time growing any type of squash in inadequate sun.

Also, my biggest concern is that it may be detrimental to the magnolia tree if you construct a raised bed around the trunk. This very likely would suffocate the feeder roots for the tree.

Maybe I've misread the post and your intentions? If so, the link below may help you pick a veggie for your shade/part sun site.

Deb

Here is a link that might be useful: growing veggies under trees

I should've mentioned that the measurements were worked around visible roots, and with plenty of space between the trunk and the raised bed! terribly sorry :) In any case, IF it's a sensible idea to try raised beds near it, what precautions should we take?

Our other option would be to build them over the concrete, but is that even possible? I'm guessing there'd be little to no drainage.

We do get some sunlight but because of the tree and the houses next to us it's not enough for squash or tomatoes. I read elsewhere that squash did grow alright in shade but thought I'd ask before making mistakes.