Transfers the sialyl group (N-acetyl-alpha-neuraminyl or NeuAc) from CMP-NeuAc onto glycoproteins and glycolipids, forming an alpha-2,6-linkage. Produces branched type disialyl structures by transfer of a sialyl group onto the GalNAc or GlcNAc residue inside backbone core chains having a terminal sialic acid with an alpha-2,3-linkage on Gal. ST6GalNAcVI prefers glycolipids to glycoproteins, predominantly catalyzing the biosynthesis of ganglioside GD1alpha from GM1b. Besides GMb1, MSGG and other glycolipids, it shows activity towards sialyl Lc4Cer generating disialyl Lc4Cer, which can lead to the synthesis of disialyl Lewis a (Le(a)), suggested to be a cancer-associated antigen (By similarity). Also has activity toward GD1a and GT1b, and can generate DSGG (disialylgalactosylgloboside) from MSGG (monosialylgalactosylgloboside) (By similarity). CMP-N-acetyl-beta-neuraminate + ganglioside GM1b (d18:1(4E)) = a ganglioside GD1alpha (d18:1(4E)) + CMP + H(+) CMP-N-acetyl-beta-neuraminate + N-acetyl-alpha-neuraminosyl-(2->3)-beta-D-galactosyl-(1->3)-N-acetyl-beta-D-glucosaminyl-(1->3)-beta-D-galactosyl-(1->4)-beta-D-glucosyl-(1<->1')-N-acyl-sphing-4-enine = CMP + H(+) + N-acetyl-alpha-neuraminosyl-(2->3)-beta-D-galactosyl-(1->3)-[N-acetyl-alpha-neuraminosyl-(2->6)]-N-acetyl-beta-D-glucosaminyl-(1->3)-beta-D-galactosyl-(1->4)-beta-D-glucosyl-(1<->1')-N-acyl-sphing-4-enine CMP-N-acetyl-beta-neuraminate + globoside MSGG = CMP + globoside DSGG + H(+) CMP-N-acetyl-beta-neuraminate + ganglioside GD1a (d18:1(4E)) = CMP + ganglioside GT1aalpha (d18:1(4E)) + H(+) CMP-N-acetyl-beta-neuraminate + ganglioside GT1b (d18:1(4E)) = CMP + ganglioside GQ1b alpha (d18:1(4E)) + H(+) 3-O-[alpha-Neu5Ac-(2->3)-beta-D-Gal-(1->3)-alpha-D-GalNAc]-L-Ser-[protein] + CMP-N-acetyl-beta-neuraminate = 3-O-{alpha-Neu5Ac-(2->3)-beta-D-Gal-(1->3)-[alpha-Neu5Ac-(2->6)]-alpha-D-GalNAc}-L-Ser-[protein] + CMP + H(+) 3-O-[alpha-Neu5Ac-(2->3)-beta-D-Gal-(1->3)-alpha-D-GalNAc]-L-Thr-[protein] + CMP-N-acetyl-beta-neuraminate = 3-O-{alpha-Neu5Ac-(2->3)-beta-D-Gal-(1->3)-[alpha-Neu5Ac-(2->6)]-alpha-D-GalNAc}-L-Thr-[protein] + CMP + H(+) Belongs to the glycosyltransferase 29 family.