External steel frame retrofitting effectively enhances the lateral resistance performance of existing reinforced concrete school buildings. However, when column shear failure occurs, ductility capacity is reduced, posing a risk of sudden collapse in high-seismic hazard areas. The purpose of this study is to propose a linear-elastic analysis-based retrofit process to reduce the likelihood of column shear failure and maximize retrofit effectiveness when applying external steel frame retrofitting. To achieve these objectives, a multiple-step process was presented and a case application was performed using quasi-static cyclic loading test results of a school building specimen retrofitted with an external steel frame system. Experimental results showed that strength, stiffness, and energy dissipation were improved by the retrofit system. However, the damage mechanism shifted from beam-column joints to column bases, resulting in reduced ductility capacity due to column shear failure. By applying the proposed process, the lateral stiffness ratio of the external steel frame columns was increased from 0.23 to 0.74, eliminating shear failure in existing reinforced concrete columns and confirming that it can contribute to improving ductility capacity.