A study done of mitochondrial DNA done in 2002 found 83% European, 5% each Native American and Subsaharan African, and 7% various kinds of Asian DNA on the maternal lines. A 2010 autosomal study, measuring everything BUT the mother's-mother's mother and father's father's father etc. lines, found matching with these triracial populations but also a lot of South and Southwest Asian, and specifically a lot of matches to Romani Gypsies. Only the 2012 Y-DNA study found a purely biracial, rather than triracial or four continent profile-- 60/40 European/African male progenitors. Absence of Native American Y is easily explained, in contrast to the equal Native American and African elements in the mitochondrial study, by the drastically different levels of Native American "miscegenation" between white males and Indian females (widespread and well-attested) and Indian males and white females (unheard-of and undocumented.)
As for more claiming than having Melungeon ancestry, that depends on how narrowly or broadly you define it. I come from a "purely and proudly White ever since 1790, despite the fact that we were called mulatto in colonial tax records" source population in eastern NC, and thus identify as Melungeon-related rather than Melungeon per se since I don't have any ancestors in Appalachia. Hundreds of thousands of "white" and "black" and "Indian" Carolinians and Virginians are Melungeon-related in this way, versus only a few thousand "Melungeon descendants" in terms of specific lineage along the VA/TN line.