The transcription factor BACH1 regulates heme homeostasis and oxidative stress responses and promotes cancer metastasis upon aberrant accumulation. Its stability is controlled by two F-box protein ubiquitin ligases, FBXO22 and FBXL17. Here we show that the homodimeric BTB domain of BACH1 functions as a previously undescribed quaternary structure degron, which is deciphered by the two F-box proteins via distinct mechanisms. After BACH1 is released from chromatin by heme, FBXO22 asymmetrically recognizes a cross-protomer interface of the intact BACH1 BTB dimer, which is otherwise masked by the co-repressor NCOR1. If the BACH1 BTB dimer escapes the surveillance by FBXO22 due to oxidative modifications, its quaternary structure integrity is probed by a pair of FBXL17, which simultaneously engage and remodel the two BTB protomers into E3-bound monomers for ubiquitination. By unveiling the multifaceted regulatory mechanisms of BACH1 stability, our studies highlight the abilities of ubiquitin ligases to decode high-order protein assemblies and reveal therapeutic opportunities to block cancer invasion via compound-induced BACH1 destabilization.