Updated project metadata. Cells adapt to ever-changing environmental cues by remodeling their inventories of multiprotein complexes. The cellular repertoire of modular multiprotein SCF (SKP1-CUL1-Fbox protein) E3 ligase complexes - which mediate much protein degradation - requires CAND1 to distribute the limiting CUL1 subunit as needed across the family of ~70 different Fbox proteins. Yet how a single assembly factor coordinately promotes dissociation of idling complexes and formation of numerous distinct multiprotein complexes as needed remains unknown. Here, we address this by obtaining cryo-EM structures of CAND1-bound SCF complexes in multiple states, and correlating effects of mutations on the conformational ensembles and in biochemical and cellular assays. The data suggest CAND1 initially clasps catalytic domains of an inactive SCF, rolls around, and allosterically rocks and destabilizes the SCF interface. New SCF production proceeds in reverse, through SKP1 and the Fbox allosterically reducing interactions with CAND1. The CAND1-SCF conformational ensemble fuels mixing-and-matching of SCF parts in response to substrate availability. Thus, our data reveal the biogenesis of a predominant family of E3 ubiquitin ligases, and the molecular basis for systemwide multiprotein complex assembly.