GO:0047224:   acetylgalactosaminyl-O-glycosyl-glycoprotein beta-1,3-N-acetylglucosaminyltransferase activity
Catalysis of the reaction: N-acetyl-D-galactosalaminyl-R + UDP-N-acetyl-D-glucosamine = N-acetyl-beta-D-glucosaminyl-1,3-N-acetyl-D-galactosaminyl-R + UDP.