The observation of a substantial interfacial Dzyaloshinskii-Moriya interaction (IDMI) in twodimensional (2D) transition-metal dichalcogenide (TMD)/ferromagnet (FM) interfaces has opened up the possibility of exploring chiral spin textures and spin dynamics in such systems. This makes the exploration of the additive IDMI in the 2D-TMD/FM/heavy-metal trilayer system an intriguing problem. Here, using the Brillouin light-scattering technique, we have demonstrated the significant contribution of the monolayer-MoS2/Co interface to enhancing the IDMI strength of a widely investigated Co/Pt interface by introducing an additive IDMI when combined to form the MoS2/Co/Pt trilayer stack. Additionally, the FM-layer-thickness-dependent study serves the dual purpose of conducting a comparative analysis of the IDMI strength between Co(t)/Pt(4) and MoS2/Co(t)/Pt(4) systems (where t= 2, 4, and 8 nm), as well as confirming the pure interfacial origin of the DMI in these systems. Our study opens up the promising possibility of using hybrid multilayers to stabilize chiral spin textures, offering potential applications in future spintronic devices.