The novel all-d-metal Ni-Mn-Ti Heusler alloys have various application prospects in the field of functional materials owing to their excellent elastocaloric effect and mechanical properties. However, the noteworthy magnetocaloric effect in conventional Ni-Mn-based Heusler alloys is not reflected in Ni-Mn-Ti alloys because of the weak magnetism of both its austenitic parent and martensitic phases. To overcome this limitation, this study explored the effect of Co and Si codoping on the martensitic transformation and magnetic and mechanical properties of Ni-Mn-Ti alloys based on first-principles calculation. The codoping of Co and Si effectively modulated the comprehensive properties of the Ni-Mn-Ti alloys. Specifically, Si atoms tended to directly occupy the Mn sublattice, whereas Co atoms tended to directly occupy the Ni sublattice. Further, the codoped Co and Si atoms exhibited a tendency of aggregated distribution in the alloy. In the Ni-(Co)-Mn-(Si)-Ti alloy, the austenite transformed from an antiferromagnetic state to a ferromagnetic state with increasing Co content. In contrast, the martensite remained in an antiferromagnetic state. This resulted in the observation of a magneto-structural transition at specific compositions, which facilitated the realization of a significant magnetocaloric effect. Furthermore, the Si-doped Ni-Mn-Ti alloy significantly increased its strength while decreasing its toughness. Whereas, the Co and Si-codoped Ni-Mn-Ti alloy exhibited better overall mechanical properties than the ternary. Finally, the study also explored the density of electronic states (DOS) of the alloys to elucidate the physical mechanisms underlying the experimentally observed martensitic transformation and the changes in the magnetic properties.