Beta-1,3-N-acetylglucosaminyltransferase that synthesizes the core 3 structure of the O-glycan, an important precursor in the biosynthesis of mucin-type glycoproteins. Plays an important role in the synthesis of mucin-type O-glycans in digestive organs. 3-O-[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-alpha-D-galactosaminyl]-L-threonyl-[protein] + H(+) + UDP 3-O-[N-acetyl-alpha-D-galactosaminyl]-L-seryl-[protein] + UDP-N-acetyl-alpha-D-glucosamine = 3-O-[N-acetyl-beta-D-glucosaminyl-(1->3)-N-acetyl-alpha-D-galactosaminyl]-L-seryl-[protein] + H(+) + UDP Protein modification; protein glycosylation. Belongs to the glycosyltransferase 31 family.