Check out the article "Complexion of Tennessee Changes," in the Tennessean. According to the article, Tennessee's multiracial population is at about 1.73 %, with the national average being 2.92%. What's significant for Tennessee is that the increase is up by 74% from the 2000 to 2010 Censuses.
The most common mixes chosen on the 2010 Census for Tennesseans were white and black, Asian and white and American Indian and white.
Military service and time spent on a college campus were two factors contributed to the changing demographic. The article also notes the historic Loving vs. Virginia decision, which legalized interracial marriage in the U.S. Another very important factor is that some folks may have chosen one race in 2000 but decided to choose more than one in 2010.
Thanks so much, Shannon, for sending me this article!