Catalysis of the reaction: 3-O-[N-acetyl-beta-D-glucosaminyl-(1->3)-N-acetyl-alpha-D-galactosaminyl]-L-threonyl-[protein] + UDP-N-acetyl-alpha-D-glucosamine = 3-O-[N-acetyl-beta-D-glucosaminyl-(1->3)-[N-acetyl-beta-D-glucosaminyl-(1->6)]-N-acetyl-alp.