Natural gas has become the dominant source of electricity in the United States, and technologies capable of efficiently removing CO2 from natural gas-fired power plants emissions could reduce their emission intensity. However, given the low partial pressure of CO2 in the flue stream, separation of CO2 is particularly challenging. Taking inspiration from the crystal structures of diamine-appended metal–organic frameworks exhibiting two-step cooperative CO2 adsorption, we report a family of robust tetraamine-functionalized frameworks that retain cooperativity, leading to the potential for exceptional efficiency in capturing CO2 under the extreme conditions relevant to natural gas flue emissions. The ordered, multimetal coordination of the tetraamines impart the materials with extraordinary stability to adsorption-desorption cycling with simulated humid flue gas and enable regeneration using low-temperature steam in lieu of costly pressure or temperature swings.