Recent findings of large anomalous Hall signal in nonferromagnetic and nonferrimagnetic materials suggest that the magnetization of the system is not a critical component for the realization of the anomalous Hall effect (AHE). Here, we present a combined theoretical and experimental study demonstrating the evolution of different mechanisms of AHE in a cubic Heusler system MnPt_1−xIr_xSn. With the help of magnetization and neutron diffraction studies, we show that the substitution of nonmagnetic Ir in place of Pt significantly reduces the net magnetic moment from 4.17 μ_B/f.u. in MnPtSn to 2.78 μ_B/f.u. for MnPt_0.5Ir_0.5Sn. In contrast, the anomalous Hall resistivity is enhanced by nearly three times from 1.6 μΩ cm in MnPtSn to about 5 μΩ cm forMnPt_0.5Ir_0.5Sn. The power law analysis of the Hall resistivity data suggests that the extrinsic contribution of AHE that dominates in the case of the parent MnPtSn almost vanishes for MnPt_0.5Ir_0.5Sn, where the intrinsic mechanism plays the major role. The experimental results are well supported by our theoretical study, which shows a considerable enhancement of the spin-orbit coupling when Ir is introduced into the system. Our finding of a crossover of the anomalous Hall effect with chemical engineering is a major contribution toward the recent interest in controlling the band topology of topological materials, both in bulk and thin-film forms.