SUMO chains act as stress-induced degradation tags or repair factor-recruiting signals at DNA lesions. Although E1 activating, E2 conjugating and E3 ligating enzymes efficiently assemble SUMO chains, specific chain-elongation mechanisms are unknown. E4 elongases are specialized E3 ligases that extend a chain but are inefficient in the initial conjugation of the modifier. We identified ZNF451, a representative member of a new class of SUMO2 and SUMO3 (SUMO2/3)-specific enzymes that execute catalysis via a tandem SUMO-interaction motif (SIM) region. One SIM positions the donor SUMO while a second SIM binds SUMO on the back side of the E2 enzyme. This tandem-SIM region is sufficient to extend a back side-anchored SUMO chain (E4 elongase activity), whereas efficient chain initiation also requires a zinc-finger region to recruit the initial acceptor SUMO (E3 ligase activity). Finally, we describe four human proteins sharing E4 elongase activities and their function in stress-induced SUMO2/3 conjugation.