As mentioned above, corn, beans and squash do very well together. My daughter did a report on the Iroquois Indians and they called these the 3 sisters. The corn gave the beans something to grow up, the beans fix Nitrogen which the corn likes and the squash has big leaves shading and inhibiting weeds. We are trying this summer.
Carrots love tomatoes! Plant them along the edges of your tomato rows! Lettuce does well in any nook or cranny, and beans and squash planted with corn saves space too. The beans go up the corn and the squash creeps at the bottom.
You can plant nearly anything together. Plant tall stuff on the north side, so it doesn't shade smaller plants. Space out the big stuff, then toss herb seeds in between (basil, parsley, dill all do well spread out like that). Put your lettuces & radishes in the front, because they'll harvest early, then you can plant a second round half-way through the summer.
The only thing I can think of that's not quite compatible with everything else is peppers. Peppers prefer a slightly more acidic ("sour") soil and most vegies prefer neutral to slightly alkaline ("sweet") soil. Put your peppers (if you like them) at one end and toss some paper match heads in the hole underneath. They'll appreciate the phosphorus. I saw that trick on Victory Garden years ago.
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