The short answer is that while the "three sisters" (maize, beans, and squash) eventually became the primary components of Southwestern agriculture (and in the Eastern Woodlands), other domesticates and wild plants like maygrass, little barley, and goosefoot/amaranth were important supplements to Native diets in the Southwest and Eastern Woodlands up until or beyond contact.

In the Southwest at least, these plants filled important niches in the subsistence strategy of agricultural groups. On the one hand you have garden weeds, like amaranth/goosefoot, that like to grow in the cultivated fields and gardens of domestic crops like maize. Instead of extirpating these "weeds", Native people used them as supplementary food sources during the growing season when maize and beans had yet to ripen.

Others, like little barley especially, filled other important seasonal gaps in subsistence. Little barley is a late winter and spring crop, a time when the major domesticates (like maize) were not yet ripe and when the stores of said crops from the previous seasons would be running low. Domestication of little barley was probably driven in part by the desire for a seasonal plant food that could be managed by humans and which was less dependent on seasonal variability (though desire for new morphological traits like a greater number of fruiting bodies per plant probably also drove domestication).

I can't really speak to the Eastern Woodlands (though a chapter in the book I recommend below indicates that chenopodium (goosefoot) has been found at Cahokia and was in use across the Eastern Woodlands). I can speak to the situation in the Southwest, however. In the Southwest, amaranth and chenopodium are found in basically every agricultural context up to the contact period, and into the early colonial period. They are an extremely ubiquitous plant in archaeological contexts.

Little barley is likewise very ubiquitous through time, but a bit more spatially restricted. Until recently, little barley was thought to only be present in southern Arizona (the Hohokam region) and along the Rio Grande and the Mogollon Rim. However, a single site on the Colorado Plateau (in the Mesa Verde region) has now produced evidence for little barley cultivation.

Maygrass is a less prevalent species in the SW (though I believe much more common in the Eastern Woodlands), but it is likewise present in most agricultural contexts throughout time.

For the most part these wild crops drop out of frequent use during the early colonial period. Partially this is because the introduction of European crops helped fill environmental and seasonal gaps in the agricultural regime of the Southwest (much like New World crops helped fill similar gaps in the agricultural regimes of the Old World). For instance, winter wheat was a highly sought after product in the American Southwest because it filled the same seasonal niche that little barley does, but with a much higher yield.

If you are interested in these indigenous domesticates (instead of the introduced domesticates of maize and beans), this edited volume covers the whole range of indigenously domesticated plants north of Mesoamerica in extensive detail, including what archaeological evidence we have for their use (e.g. how long they were used for and what kind of geographic range). It's pretty much the authoritative text on the issue, with the most up-to-date information on the topic.

Hope that helps answer your question!