The Ufd1/Npl4/Cdc48 complex is a universal protein segregase that plays key roles in eukaryotic cellular processes. Its functions orchestrating the clearance or removal of polyubiquitylated targets are established; however, prior studies suggest that the complex also targets substrates modified by the ubiquitin-like protein SUMO. Here, we show that interactions between Ufd1 and SUMO enhance unfolding of substrates modified by SUMO-polyubiquitin hybrid chains by the budding yeast Ufd1/Npl4/Cdc48 complex compared to substrates modified by polyubiquitin chains, a difference that is accentuated when the complex has a choice between these substrates. Incubating Ufd1/Npl4/Cdc48 with a substrate modified by a SUMO-polyubiquitin hybrid chain produced a series of single-particle cryo-EM structures that reveal features of interactions between Ufd1/Npl4/Cdc48 and ubiquitin prior to and during unfolding of ubiquitin. These results are consistent with cellular functions for SUMO and ubiquitin modifications and support a physical model wherein Ufd1/Npl4/Cdc48, SUMO, and ubiquitin conjugation pathways converge to promote clearance of proteins modified with SUMO and polyubiquitin.