Targeted protein degradation is a drug modality represented by compounds that recruit a target to an E3 ubiquitin ligase to promote target ubiquitination and proteasomal degradation. Historically, the field distinguishes monovalent degraders from bifunctional degraders (PROTACs) that connect target and ligase via separate binding ligands joined via a linker1-4. Here, we elucidate the mechanism of action of a PROTAC-like degrader of the transcriptional coactivator BRD4, composed of a BRD4 ligand linked to a ligand for the E3 ligase CRL4DCAF15. Using orthogonal CRISPR/Cas9 screens we identify the degrader activity is independent of DCAF15, and relies on a different CRL4 substrate receptor, DCAF16. We demonstrate an intrinsic affinity between BRD4 and DCAF16, which is dependent on the tandem bromodomains of BRD4 and further increased by the degrader without physically engaging DCAF16 in isolation. Structural characterization of the resulting ternary complex reveals both BRD4 bromodomains are bivalently engaged in cis by the degrader and are bound to DCAF16 through several interfacial BRD4-DCAF16 and degrader-DCAF16 contacts. Our findings demonstrate that intramolecularly bridging domains can confer glue-type stabilization of intrinsic target-E3 interactions, and we propose this as a general strategy to modulate the surface topology of target proteins to nucleate co-opting of E3 ligases or other cellular effector proteins for effective proximity-based pharmacology.