The design of stable adsorbents capable of selectively capturing dioxygen with a high reversible capacity is a crucial goal in functional materials development. Drawing inspiration from biological O₂ carriers, we demonstrate that coupling metal-based electron transfer with secondary coordination sphere effects in the metal-organic framework Co₂(OH)₂(bbta) (H₂bbta = 1H,5H-benzo(1,2-d:4,5-d')bistriazole) leads to strong and reversible adsorption of O₂. In particular, moderate-strength hydrogen bonding stabilizes a cobalt(III)-superoxo species formed upon O₂ adsorption. Notably, O₂-binding in this material weakens as a function of loading, as a result of negative cooperativity arising from electronic effects within the extended framework lattice. This unprecedented behavior extends the tunable properties that can be used to design metal-organic frameworks for adsorption-based applications.