The whole three sisters thing was an early crop rotation method. Not all together like as advertised.
Beans where grown first as they are shallow rooted and produce about 50% of the nitrogen they need. If they harvest 25% of the crop and till under the rest they have around around a 25% increase in a available N.
The next season is corn and pumpkins together. They are both heavy N feeders. They spaced out the corn a lot more than modern hybrids so the pumpkins had plenty of room to grow and shade out weeds. They unfortunately share the pest of cucumber beetle species (corn rootworm).
The next season they had to go back to beans to break the rootworm cycle.
Eventually other nutrients would become low (P,K, micros etc). Other pests and diseases would buildup. They would rotate onto new plots letting the old plots go fallow for a while.