The propagation speeds and flammability limits of cool flames are numerically simulated at elevated pressures and with dilutions for dimethyl ether mixtures. The results showed that there are three different flame regimes, hot flame, double flame, and cool flame. The cool flames exist on both fuel lean and fuel rich sides and thus dramatically extend the lean and rich flammability limits of hot flames. Pressure and dilution have a significant impact on the flame speed, flammable limit, and structure of cool flames. On the fuel lean side, the cool flame propagation speed decreases significantly with pressure. However, the cool flame speed on the fuel rich side is much less affected by the pressure. At a lower pressure, the transition from hot flame to cool flame is an extinction transition at the hot flame flammability limit. However, at high pressure, due to the increase of fuel reactivity and the decrease of flame speed of cool flames, it is found that there is a direct transition between cool flame and hot flame without an extinction limit. A K-shaped flammability diagram including both cool flames and hot flames is obtained. Moreover, it is also found that the increase nitrogen dilution in oxidizer dramatically narrows the flammable region of hot flame but extends the flammable region of cool flames. The present study demonstrates that cool flame dynamics needs to be appropriately included for modeling high pressure and near limit combustion of gasoline, diesel, and jet fuels in advanced engines.