I was waiting for someone else to chime in on your plan before commenting, but it seems no one wants to take a shot at it. In that case...

I think this plan looks crazy, if I am interpreting your chart correctly.

The melons and squash will easily take up 2+ sq. ft per plant, but you also have corn and beans growing in the same space. This might work if you plant the corn way before the other stuff. I've never tried anything like this before, but I'm thinking the pole beans and the squash/melons are going to compete with one another and neither plant is going produce an optimal harvest.

How are you planning on harvesting the plants in the middle of the grid once you have establish vines growing everywhere? It's going to be hard to get to the corn/beans in the middle of the plot without stepping on your bed and potentially damaging plants as well.

I may just be reading your chart wrong. If that's the case, you'll have to explain it to me a little better (I'm slow). But if I am reading your plan correctly, I think you should space things out quite a bit more. I would personally dedicate at least 2 sq. ft. for each melon/squash plant that you intended to grow, and give each corn plant at least 8" between plants (or, at most, 2 corn plants per sq. ft.).

As far as the pole beans are concerned, I've no experience using corn as a trellis for pole beans myself, but I've read many posts on this very forum that claim that it isn't usually very successful. I personally have had great success growing either plant apart from one another, and I see no reason to squeeze them together to compete for nutrients.

If you are a very experienced gardener and you are into experimenting or a challenge, then by all means, go ahead with your plan and let us know how it goes. If you are just a beginner/novice gardener, I would save yourself the trouble and just do a more conservative garden setup. It's better to start small and harvest at least something, than to try unrealistic plans and then get overwhelmed with the sheer amount of vegetation that comes from it.

Again, just my opinion. Anyone else with more experience is welcome to chime in and correct me.

I agree with triplelione - you are pushing it to get all those veggies in that space and it will be impossible to harvest unless you save room for a walkway down the middle. I worry about the corn being spaced throughout the plot and whether it will get proper pollination. But what the heck, try it and then you will know if it will work. Experimenting with different things in the garden is the fun part of growing.

1.to many melons and squash.
2. climbing bean will pull ears of corn
3. the 3 sisters method was design for winter squash vining squash, corn for meal, bean for drying
4. sweet corn, summer squash and fresh string beans are entirely unsuitable for the system
5. if want do three sister use bush squash, bush beans sweet
6 you whole plan is to close together do get decent results.
I could go on. but won't

If I were you, I would plant the melons in every other square vice every square giving them more room to run. The will provide the dhade for the soil. Then in the next row of squares where in the horizontal row where there is no melon plant a bush squash. Use plenty of fertilizer. In this manner you can get all of the plants you want and get the benefit of 3 sisters companion planting.