What's likely is that many groups came here, but in relatively small numbers. Europeans crossed by skirting the North Atlantic pack ice. Some Asians did the same along the Nothern Pacific pack ice as well. Africans crossed the Atlantic Narrows, which would have been narrower still during the Pleistocene. The European migrants were likely the source of the Clovis tool tradition. Yes, there are notable differences between Solutrean and Clovis, but no similar stone tool styles exist in Asia. Also, these original populations were likely small.
When the Asians entered later, they encountered people already living in the Americas. If all parties were hunter/gatherers, then the meeting was probably peaceful. (It's the agriculturalists that tend to get violent.) The rapid adoption of the Clovis style tools may indicate trade resulting from such friendly relations. (And there is evidence that the Clovis technology spread out of the Northeast rather than out of the Southwest.) They would have simply interbred with the existing populations. If the Asians were more numerous, then of course their descendents would have a more Asiatic appearence.
The multiple migration theory solves a few sticky problems. One of those is the question of how Paleo-indians got to the tip of South America in such short order. It's presumed that the "migration" was really the pre-historic version of urban sprawl. People slowly diffused into the Americas in search of new hunting grounds. Hunter/gatherer villages can only get so big before they start to overhunt an area. When this happens, the village splits and the new group has to find its own territory. This moves the line of advance several miles every few generations. But this doesn't explain how they could have diffused from Beringia to Monte Verde in 2,500 years. (Or, depending upon what dating one uses, how they could have gone backwards in time!) However, diffusion from the Atlantic Narrows to Monte Verde in 6,500 years is far more believable.
Oh yeah. Hunters and gatherers always welcome new groups into their hunting territories!
;^)
There had been populations in South America of much the same races now living there (natives) certainly over 30M years BP and probably to 40M or very, very close to that...
These involving persons having descendants in the present day, my old caveat. Not dead-end shipwreck victims who may have lived a few generations, or even some very old homo erectus (Calico) who must have perished to the last man or woman after awhile...
Democrats are thought to be such friends of science as opposed to theology, while Republicans are just "dumb." Yet it was the Democrats who refused to study or look at Kennewick Man, and buried his finding site under 500 tons of concrete! They are afraid of what they might find, they are the theologians and dogmatists of our age, trembling at ever new discovery, for they know their beliefs will not stand examination.