I'm not aware of any research studies that have looked at this, but the consensus seems to be that multi-bearded birds are probably not only the result of genetics but likely the rare genetic offspring result of a tom breeding a bearded hen. The places I've hunted holding multi-bearded toms have also been the places where I've seen more than one bearded hen...

Funny thing is that one year in CT I harvested a double-bearded jake that I thought was a tom. He came in on string, all by himself, and the 6" and 5.5" beards were far enough apart on his breast that when they hung together he looked like a longbeard. I still remember the ~45 yd shot that dropped him on the edge of a creek. He never went into strut on his way in, and I was damn surprised when I got on him and saw the nubs and uneven fan. He filled 1 of my 3 tags and he didn't score very high but he sure was tasty...