Understanding the fundamental characteristics of high-pressure cool flames is crucial for the development of advanced and efficient low-temperature combustion engine technologies. The pressure dependency of multi-oxygen addition branching reactions in low-temperature chemistry significantly influences the dynamics, structure, and reactivity of cool flame. This study investigates the non-premixed cool flame of diethyl ether (DEE) at elevated pressures. The results show that pressure rise promotes low-temperature chemistry and significantly extends the extinction limit of cool flame. It is found that the cool flame heat release rate is correlated with the product of pressure and the square root of the pressure-weighted strain rate, Q∼aP·P, which is different from that of hot flames, Q∼aP. The radical index concept for atmospheric cool flames is extended to high-pressure cool flames allowing to decouple the mass and thermal transports from the chemical kinetics term to evaluate the fuel reactivity at elevated pressures. The radical index shows that the low-temperature reactivity of DEE is enhanced with the pressure and is higher than n-dodecane by a factor of 19, 18.3, and 16.4 for 1, 3, and 5 atm, respectively. Kinetic analysis reveals that pressure rise results in QOOH stabilization and promotions of the second O2 addition and the chain-branching reaction pathway for multiple OH radical productions.