Heterobifunctional small-molecule degraders that induce protein degradation through ligase-mediated ubiquitination have shown considerable promise as a new pharmacological modality. However, we currently lack a detailed understanding of the molecular basis for target recruitment and selectivity, which is critically required to enable rational design of degraders. Here we utilize a comprehensive characterization of the ligand-dependent CRBN–BRD4 interaction to demonstrate that binding between proteins that have not evolved to interact is plastic. Multiple X-ray crystal structures show that plasticity results in several distinct low-energy binding conformations that are selectively bound by ligands. We demonstrate that computational protein–protein docking can reveal the underlying interprotein contacts and inform the design of a BRD4 selective degrader that can discriminate between highly homologous BET bromodomains. Our findings that plastic interprotein contacts confer selectivity for ligand-induced protein dimerization provide a conceptual framework for the development of heterobifunctional ligands.