Transfers the sialyl group (N-acetyl-alpha-neuraminyl or NeuAc) from CMP-NeuAc to the GalNAc residue on the NeuAc-alpha-2,3-Gal-beta-1,3-GalNAc sequence of glycoproteins and glycolipids forming an alpha-2,6-linkage. Produces branched type disialyl structures by transfer of a sialyl group onto a GalNAc residue inside the backbone core chains. ST6GalNAcIII prefers glycolipids to glycoproteins, predominantly catalyzing the biosynthesis of ganglioside GD1alpha from GM1b (PubMed:16169874, PubMed:17123352). GD1alpha is a critical molecule in the communication and interaction between neuronal cells and their supportive cells, particularly in brain tissues, and functions as an adhesion molecule in the process of metastasis (By similarity). Sialylation of glycoproteins or glycosphingolipids is very important in tumor development, neuronal development, nerve repair, immunological processes and regulation of hormone sensitivity (PubMed:17123352).