Beta-1,3-N-acetylgalactosaminyltransferase that synthesizes a unique carbohydrate structure, GalNAc-beta-1-3GlcNAc, on N- and O-glycans. Has no galactose nor galactosaminyl transferase activity toward any acceptor substrate. Involved in alpha-dystroglycan (dag1) glycosylation. 3-O-(N-acetyl-beta-D-glucosaminyl-(1->4)-alpha-D-mannosyl)-L-threonyl-[protein] + UDP-N-acetyl-alpha-D-galactosamine = 3-O-[beta-D-GalNAc-(1->3)-beta-D-GlcNAc-(1->4)-alpha-D-Man]-L-Thr-[protein] + H(+) + UDP Protein modification; protein glycosylation. Belongs to the glycosyltransferase 31 family.