The Amish don't read agronomy books. They know which plants to grow together because they've observed it for 300 years.
Three Sisters
Corn + beans + squash — a Native American classic adopted by the Amish. Corn supports beans. Beans fix nitrogen for corn. Squash covers soil with leaves — suppressing weeds and retaining moisture. Three plants feed each other.
Good Neighbors
Tomatoes + basil — basil repels aphids and whiteflies. Carrots + onions — onion smell drives off carrot fly, carrots repel onion fly. Cabbage + dill — dill attracts beneficial insects (ladybugs). Beans + potatoes — beans provide nitrogen.
Enemies
Tomatoes + cabbage — both heavy feeders, compete for resources. Fennel — enemy to almost everything, plant separately. Onions + beans — onions suppress bean growth. Potatoes + tomatoes — same diseases (blight).
Why It Works
Different root systems draw nutrients from different depths. Scents of some plants mask others from pests. Flowers attract pollinators to the whole bed.