There is absolutely no way, it is not a vining crop. I grew patty-pans 2 years ago and they were wonderful to eat. I planted it at the corner of a 4 x 4 bed hoping that it would take up less space of my bed since some would be overlapping the sides. That plant could have easily taken up 8 square feet. If you have seen an older version of Mel's book with a picture of a butternut squash in a bed, that is about how big that plant was.

I tried a zuch that way once. It didn't work out. The weight of the leaves would bend the hollow stems down over the wire of the tomatoe cage and that cut off circulation to the leaf, which then died. This caused the plant to struggle and I got like 2 zuch's total from it all summer. Bad plan. Abort, Abort!

I plant my summer squash in the center of 4 square feet (2x2)and let them trail over the side of the raised bed. Snibb, a poster to this sight has had luck training them up a single stake. I believe a metal fence post is used and a jump rope or equivelent thickness cord is used to tie up the central stem of the squash plant as it grows, knotting every 8 inches up or so. With this method, Snibb only gives it one square foot of space, but I think other shorter plants are located in the surrounding squares.

Hope that helps!
Susan