Cooperative adsorption of gases by porous frameworks, which permits more efficient uptake and removal than the more usual noncooperative (Langmuir-type) adsorption, usually results from a phase transition of the framework. Here we show how cooperativity emerges in the class of metal-organic frameworks mmen-M_{2}(dobpdc) in the absence of a phase transition. Our study provides a microscopic understanding of the emergent features of cooperative binding, including the position, slope, and height of the isotherm step, and indicates how to optimize gas storage and separation in these materials.