Ubiquitin-dependent proteolysis regulates diverse cellular functions with high substrate specificity. The precision of this regulatory mechanism hinges on the ability of ubiquitin E3 ligases to decode the targets’ degradation signals, i.e. degrons, which canonically present as short linear motifs. Here we show that BACH1, a transcription repressor of antioxidant response genes, features two distinct unconventional degrons encrypted in the quaternary structure of its homodimeric BTB domain. These two degrons are both functionalized by oxidative stress and are deciphered by two complementary E3s. FBXO22 recognizes a degron constructed by the BACH1 BTB domain dimer interface, which is unmasked from the co-repressor NCOR1 after BACH1 is released from chromatin by excessive heme. When this degron is impaired by oxidation, a second BACH1 degron embodied by the resulting BTB dimer with compromised integrity is probed by a pair of FBXL17 that remodels the two BTB protomers into E3-bound monomers for ubiquitination. Our findings reveal the remarkable multidimensionality of protein degradation signals underpinning substrate selectivity and functional versatility of ubiquitin-dependent proteolysis.