Glycosyltransferase that catalyzes the transfer of an N-acetylglucosamine (GlcNAc) moiety in beta1-6 linkage from UDP-GlcNAc onto mucin-type core 1 O-glycan to form the branched mucin-type core 2 O-glycan. The catalysis is metal ion-independent and occurs with inversion of the anomeric configuration of sugar donor (PubMed:9490652) (By similarity). Selectively involved in synthesis of mucin-type core 2 O-glycans that serve as scaffolds for the display of selectin ligand sialyl Lewis X epitope by myeloid cells, with an impact on homeostasis and recruitment to inflammatory sites (By similarity). Can also act on glycolipid substrates. Transfers GlcNAc moiety to GalGb4Cer globosides in a reaction step to the synthesis of stage-specific embryonic antigen 1 (SSEA-1) determinant (By similarity). Can use Galbeta1-3GalNAcalpha1- and Galbeta1-3GalNAcbeta1- oligosaccharide derivatives as acceptor substrates (By similarity). O(3)-[beta-D-galactosyl-(1->3)-N-acetyl-alpha-D-galactosaminyl]-L-seryl-[protein] + UDP-N-acetyl-alpha-D-glucosamine = 3-O-{beta-D-galactosyl-(1->3)-[N-acetyl-beta-D-glucosaminyl-(1->6)]-N-acetyl-alpha-D-galactosaminyl}-L-seryl-[protein] + H(+) + UDP O(3)-[beta-D-galactosyl-(1->3)-N-acetyl-alpha-D-galactosaminyl]-L-threonyl-[protein] + UDP-N-acetyl-alpha-D-glucosamine = 3-O-{beta-D-galactosyl-(1->3)-[N-acetyl-beta-D-glucosaminyl-(1->6)]-N-acetyl-alpha-D-galactosaminyl}-L-threonyl-[protein] + H(+) + UDP globoside GalGb4Cer + UDP-N-acetyl-alpha-D-glucosamine = globoside GlcNAc-(beta1->6)-GalGb4Cer + H(+) + UDP ganglioside GA1 + UDP-N-acetyl-alpha-D-glucosamine = ganglioside beta-DGlcNAc-(1->6)-GA1 + H(+) + UDP Protein modification; protein glycosylation. Glycolipid biosynthesis. Interacts with GOLPH3; may control GCNT1 retention in the Golgi. Also detected in the trans-Golgi network. Expressed in tracheal submucosal glands and epithelium (at protein level). Belongs to the glycosyltransferase 14 family.