The quest for efficient utilization of solar light for the generation of hydrogen through water splitting has provided motivation to find new dopant elements for the wide band gap photocatalyst. In the present study, we have considered doping with pentavalent transition-metal elements, like V, Nb, and Ta, in combination with one more anionic dopant (N) or cationic dopant (Na/K/Rh) into the crystal structure of SrTiO3. Here, we present a systematic investigation of the effect of dopant element individually as well as in combination on the electronic structure of SrTiO3, using the more reliable hybrid density functional theory. Although monodoping with V, N, or Rh reduces the band gap, it may accelerate the electron hole recombination rate due to introduction of strongly localized midgap states. However, these defect states have been found to be completely passivated in the codoped systems. Moreover, being a charge-compensated system the vacancy-related charge carrier loss is expected to be minimal in these codoped systems. All the codoped systems studied here are found to meet the thermodynamic criteria for overall water splitting due to appropriate band edge alignment with respect to the water redox levels. Among the codopant pairs, the (V/Nb/Ta, Rh) one has been found to be most effective in reducing the band gap of SrTiO3 by a significant extent. In particular, among the doped SrTiO3 with overall water-splitting capabilities, the calculated band gap for (V, Rh)-codoped SrTiO3 is the lowest reported to date.