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 acceptor through alpha-2,8- linkages (Probable) (PubMed:10766765, PubMed:11744634, PubMed:9054414, PubMed:9774483). Therefore, participates in polysialic acid synthesis on various sialylated N-acetyllactosaminyl oligosaccharides (alpha-2,3-, alpha-2,6-, or alpha-2,8-linked sialic acid), including NCAM1, NCAM1 N-glycans, FETUB N-glycans, and to a lesser extent sialylparagloboside (SPG) and AHSG, which does not require the initial addition of an alpha 2,8-sialic acid (Probable) (PubMed:7559389). However, does not exhibit sialic acid-polymerase activity (By similarity). Catalyzes polysialic acid synthesis in the hippocampal on NCAM1 and supports neurite outgrowth (PubMed:9054414). ST8SIA2-mediated polysialylation influences on oligodendrocyte differentiation and may promote the integrity of myelin and axons (By similarity). {ECO:0000250|UniProtKB:O35696, ECO:0000269|PubMed:10766765, ECO:0000269|PubMed:11744634, ECO:0000269|PubMed:7559389, ECO:0000269|PubMed:9054414, ECO:0000269|PubMed:9774483, ECO:0000305|PubMed:28810663}. This is the function of ST8SIA2 (ST8 alpha-N-acetyl-neuraminide alpha-2,8-sialyltransferase 2, ENSG00000140557).