We have investigated the energetic stability and the electronic properties of metal-organic topological insulators bilayers (BLs), (MC4S4)3-BL, with M=Ni and Pt, using first-principles calculations and tight-binding model. Our findings show that (MC4S4)3-BL is an appealing platform to perform electronic band structure engineering, based on the topologically protected chiral edge states. The energetic stability of the BLs is ruled by van der Waals interactions; being the AA stacking the energetically most stable one. The electronic band structure is characterized by a combination of bonding and anti-bonding kagome band sets (KBSs), revealing that (NiC4S4)3-BL presents a Z2-metallic phase, whereas (PtC4S4)3-BL may present both Z2-metallic phase or quantum spin Hall phase. Those non-trivial topological states were confirmed by the formation of chiral edge states in (MC4S4)3-BL nanoribbons. We show that the localization of the edge states can be controlled with a normal external electric field, breaking the mirror symmetry. Hence, the sign of electric field selects in which layer each set of edge states are located. Such a control on the (layer) localization, of the topological edge states, bring us an additional and interesting degree of freedom to control the transport properties in layered metal-organic topological insulator.