That's a pretty high corn yield. I'd only count on a crop like that if I could be sure of ideal conditions.....an adapted variety, really rich soil, adequate moisture, no major bug attacks, etc.
The bean vines will tangle the cornstalks together into a jungle, and the squash cover the ground likewise. You'll have trouble getting into the mess to harvest any of the three in an immature state. The only way I would try it is to lay it out in long "beds" with fairly wide access pathways which you could go along and reach into the corn for access.
Sweet corn is often shorter-stalked than the old heirloom field corns traditionally used. I've shored up cornstalks for heavy bean and
pea vines by tying together three or four adjacent stallks at the top, in the form of a tipi, which makes a stronger scaffold. Another way, which also improves access, is to plant the corn in groups of three or four, and then leave 3-4 feet of space each way to the next clump. The beans will then climb the corn stalks as a group and tie them together on their own. But this assumes you have enough space.
The other key is timing. Plant the corn first and let it get a foot tall or more before adding the others. That way it can stay ahead of the beans as they grow up and not get broken down in the overwhelm.....
"Three Sisters" wasn't always just three. At different times and places other things were added, sunflowers being the first to come to mind. These would add additional strong supports for bean vines.