Catalysis of the reaction: UDP-N-acetyl-D-glucosamine + N-acetyl-beta-D-glucosaminyl-1,2-alpha-D-mannosyl-1,3(6)-(N-acetyl-beta-D-glucosaminyl-1,2-alpha-D-mannosyl,1,6(3))-beta-D-mannosyl-1,4-N-acetyl-beta-D-glucosaminyl-R = UDP + N-acetyl-beta-D-glucosaminyl-1,2-(N-acetyl-beta-D-glucosaminyl-1,6)-1,2-alpha-D-mannosyl-1,3(6)-(N-acetyl-beta-D-glucosaminyl-1,2-alpha-D-mannosyl-1,6(3))-beta-D-mannosyl-1,4-N-acetyl-beta-D-glucosaminyl-R. Only branched mannose glycopeptides with non-reducing N-acetylglucosamine terminal residues act as acceptors.