Synthesizes the galactose-alpha(1,3)-galactose group by catalyzing the transfer of a galactose residue, with an alpha-1,3 linkage, on terminal lactosaminide (Gal-beta-1,4-GlcNAc-R) disaccharide borne by a glycoprotein or a glycolipid. Preferentially glycosylates proteins, can synthesize galactose-alpha(1,3)-galactose on glycoproteins but cannot synthesize the glycosphingolipid isoglobotrihexosylceramide or isogloboside 3 (iGb3). a beta-D-galactosyl-(1->4)-N-acetyl-beta-D-glucosaminyl derivative + UDP-alpha-D-galactose = an alpha-D-galactosyl-(1->3)-beta-D-galactosyl-(1->4)-N-acetyl-beta-D-glucosaminyl derivative + H(+) + UDP Binds 1 Mn(2+) ion per subunit. Protein modification; protein glycosylation. Membrane-bound form in trans cisternae of Golgi. Dorsal root ganglia neurons (at protein level). Expressed in the heart, brain, spleen, kidney, lung and liver. The conserved DXD motif is involved in cofactor binding. The manganese ion interacts with the beta-phosphate group of UDP and may also have a role in catalysis (By similarity). Belongs to the glycosyltransferase 6 family.