This study investigates the effects of oxidizer composition on stability and combustion and emission characteristics of stratified premixed CH4-O2-CO2 flames in a dual annular counter-rotating swirl (DACRS) burner for wider near blowout operability of gas turbines. Flame stratification was achieved by dividing the incoming reactants into primary and secondary streams of different oxygen fractions (OF). The effects of primary and secondary OFs (primary OFs: 60%, 50%, and 30%; and secondary OFs: 60%, 50%, 40%, and 30%) were numerically investigated at fixed inlet throat velocities and equivalence ratios (φ) of the primary and the secondary streams of 6 m/s and 2 m/s and of 0.9 and 0.55, respectively. The probability distribution function has been used to average the thermochemical properties and reaction rates. Two distinct flame shapes, the v-shaped and the conical-shaped were identified as a function of the oxidizer composition. V-shaped flames with enhanced flow mixing, strong inner and outer recirculation zones (IRZ and ORZ), and intensive interactions between both streams at lower Damkohler number (Da) were recorded for OFs within 30–50%. This indicates the ability of the DACRS burner to extend the lean blowout limit by holding stratified stable flames of lower OFs. The flame shape turned into a conical shape at OFs of 60–60% for both streams, the IRZ disappeared, intensive reaction rates of higher Da attained, and the flashback mechanism approached. Weak flame/flow interactions were observed at OFs higher than 50% with excessive combustion temperature near the burner tip. CH4 disappeared very close to the burner tip, indicating fast reactions.