Anomalous Hall effect (AHE) can be induced by intrinsic mechanism due to the band Berry phase and extrinsic one arising from the impurity scattering. The recently discovered magnetic Weyl semimetal Co3Sn2S2 exhibits a large intrinsic anomalous Hall conductivity (AHC) and a giant anomalous Hall angle (AHA). The predicted energy dependence of the AHC in this material exhibits a plateau at 1000 {Omega}-1 cm-1 and an energy width of 100 meV just below EF, thereby implying that the large intrinsic AHC will not significantly change against small-scale energy disturbances such as slight p-doping. Here, we successfully trigger the extrinsic contribution from alien-atom scattering in addition to the intrinsic one of the pristine material by introducing a small amount of Fe dopant to substitute Co in Co3Sn2S2. Our experimental results show that the AHC and AHA can be prominently enhanced up to 1850 {Omega}-1 cm-1 and 33%, respectively, owing to the synergistic contributions from the intrinsic and extrinsic mechanisms as distinguished by the TYJ model. In particular, the tuned AHA holds a record value in low fields among known magnetic materials. This study opens up a pathway to engineer giant AHE in magnetic Weyl semimetals, thereby potentially advancing the topological spintronics/Weyltronics.