The coadsorption of CO 2 /CH 4 in the breathing MIL-53(Cr) under the application of an additional mechanical pressure is investigated through the use of an extended thermodynamic mean-field model. The focus is on the breathing behavior, negative gas adsorption (NGA), and selective adsorption of CO 2 as well as to what degree the application of mechanical pressure influences this behavior. To this end, phase diagrams, coadsorption isotherms are constructed and the CO 2 /CH 4 selectivity is computed in terms of the vapor pressure of methane and carbon dioxide as well as the mechanical pressure. As a result, it is found that NGA can be induced by coadsorption of CO 2 /CH 4 gas mixtures with certain molar compositions. Finally, a specific adsorption/desorption cycle, which includes the application of an additional mechanical pressure, is proposed to allow for an increased CO 2 /CH 4 selectivity as well as for an expected less energy demanding CO 2 desorption step.