One illustrative method disclosed herein includes, among other things, forming a plurality of trenches that define a fin, performing a plurality of epitaxial deposition processes to form first, second and third layers of epi semiconductor material around an exposed portion of the fin, removing the first, second and third layers of epi semiconductor material from above an upper surface of the fin so as to thereby expose the fin, selectively removing the fin relative to the first, second and third layers of epi semiconductor material so as to thereby define two fin structures comprised of the first, second and third layers of epi semiconductor material, and forming a gate structure around a portion of at least one of the fin structures comprised of the first, second and third layers of epi semiconductor material.