Multi-junction (MJ) solar cells are one of the most promising technologies achieving high sunlight to electricity conversion efficiency. Resistive losses constitute one of the main underlying mechanisms limiting their efficiency under high illumination. In this paper, we study, by numerical modeling, the extent to which a fine-tuning of the different electronic gaps involved in MJ stacks may mitigate the detrimental effects of series resistance losses for concentration-dependent and independent series resistances. Our results demonstrate that appropriate bandgap engineering may lead to significantly higher conversion efficiency at illumination levels above ~1000 suns and series resistance values typically exceeding 0.02 Ω cm2, due to lower operating current and, in turn, series resistance losses. The implications for future generations of solar cells aiming at an improved conversion of the solar spectrum are also addressed.