The ubiquitin-proteasome system (UPS) is responsible for the bulk of protein degradation in eukaryotic cells, but the factors that cause different substrates to be unfolded and degraded to different extents are still poorly understood. We previously showed that polyubiquitinated substrates were degraded with greater processivity (with a higher tendency to be unfolded and degraded than released) than ubiquitin-independent substrates. Thus, even though ubiquitin chains are removed before unfolding and degradation occur, they affect the unfolding of a protein domain. How do ubiquitin chains activate the proteasome's unfolding ability? We investigated the roles of the three intrinsic proteasomal ubiquitin receptors - Rpn1, Rpn10 and Rpn13 - in this activation. We find that these receptors are required for substrate-mediated activation of the proteasome's unfolding ability. Rpn13 plays the largest role, but there is also partial redundancy between receptors. The architecture of substrate ubiquitination determines which receptors are needed for maximal unfolding ability, and, in some cases, simultaneous engagement of ubiquitin by multiple receptors may be required. Our results suggest physical models for how ubiquitin receptors communicate with the proteasomal motor proteins.