• Combined approach using pilot injection and outer nozzle fuel staging effectively controls combustion instability. • Two fuel staging methods alter flame structures, affecting time delay characteristics. • MIMO thermoacoustic model successfully predicts experimental trends. • Stability map demonstrates combined fuel staging effects on combustion instability. Hydrogen co-firing and lean premixed combustion technologies in modern gas turbines have significantly increased concerns regarding combustion instability. Although fuel staging has emerged as an effective control method, existing studies have focused on individual staging approaches, limiting our understanding of the combined staging effects. In this study, a comprehensive thermoacoustic stability map was developed by simultaneously applying outer nozzle fuel staging and pilot injection under 30% hydrogen co-firing conditions, providing a predictive framework for multiparameter instability control. An integrated methodology combining experiments, computational fluid dynamics (CFD), and thermoacoustic modeling was employed to investigate the interaction effects between the pilot injection and outer nozzle fuel staging. Experimental investigations revealed that the combined effects of pilot injection and outer nozzle fuel staging on dynamic pressure amplitudes exhibited complex interdependencies that varied with operating conditions. CFD analysis identified the underlying physical mechanisms and showed that different staging parameters modify the flame structure and time delay characteristics of the outer nozzles in distinct ways. A multi-input multi-output (MIMO) thermoacoustic model was developed to construct a stability map that incorporates the time-delay variations of outer nozzles. The stability map successfully captured the effects of pilot injection and outer nozzle fuel staging on the combustion instability characteristics. This integrated framework provides a practical design tool for optimizing fuel staging strategies in hydrogen-compatible gas turbines.