Adsorbents able to uptake large amounts of gases within a narrow range of pressure, , phase-change adsorbents, are emerging as highly interesting systems to achieve excellent gas separation performances with little energy input for regeneration. A recently discovered phase-change metal-organic framework (MOF) adsorbent is F4_MIL-140A(Ce), based on Ce and tetrafluoroterephthalate. This MOF displays a non-hysteretic step-shaped CO adsorption isotherm, reaching saturation in conditions of temperature and pressure compatible with real life application in post-combustion carbon capture, biogas upgrading and acetylene purification. Such peculiar behaviour is responsible for the exceptional CO/N selectivity and reverse CO/CH selectivity of F4_MIL-140A(Ce). Here, we combine data obtained from a wide pool of characterisation techniques - namely gas sorption analysis, infrared spectroscopy, powder X-ray diffraction, X-ray absorption spectroscopy, multinuclear solid state nuclear magnetic resonance spectroscopy and adsorption microcalorimetry - with periodic density functional theory simulations to provide evidence for the existence of a unique cooperative CO adsorption mechanism in F4_MIL-140A(Ce). Such mechanism involves the concerted rotation of perfluorinated aromatic rings when a threshold partial pressure of CO is reached, opening the gate towards an adsorption site where CO interacts with both open metal sites and the fluorine atoms of the linker.