Catalyzes the transfer of a sialic acid from a CMP-linked sialic acid donor onto a terminal alpha-2,3-, alpha-2,6-, or alpha-2,8-linked sialic acid of an N-linked glycan protein acceptor through alpha-2,8-linkages (PubMed:10766765, PubMed:11279095, PubMed:28810663, PubMed:9774483). Therefore, participates in polysialic acid synthesis on various sialylated N-acetyllactosaminyl oligosaccharides, including NCAM1 N-glycans, FETUB N-glycans and AHSG (PubMed:10766765, PubMed:11279095, PubMed:28810663, PubMed:9774483). It is noteworthy that alpha-2,3-linked sialic acid is apparently a better acceptor than alpha-2,6-linked sialic acid (PubMed:9774483).