When a conductive polymer is blended with commodity polymers such as polyolefins and/or polystyrene (PS) as a ternary blend, it has a tendency to form the core phase due to its high interfacial tension with the other components. This can limit its capacity to reduce resistivity compared to situating it at the interface. In this work, starting with a ternary low-density polyethylene/polystyrene/poly(ether-block-amide) (LDPE/PS/PEBA) blend, we examine the influence of the conductive PEBA concentration on morphology and resistivity when it exists as a core phase. Then, the hierarchical structuring of the PEBA phase will be modified through two strategies: by the addition of a fourth phase (polyethylene terephthalate (PET) or polyvinylidene fluoride (PVDF)) and by the addition of a copolymer interfacial modifier to the LDPE/PS/PEBA blend. Each of these approaches is shown to be capable of allowing the conductive PEBA to form a percolated structure assembled at the interface of two other continuous phases. The completely wet layered structuring of PEBA between PS and PVDF in the quaternary LDPE/PS/PEBA/PVDF blend leads to an exceptionally low percolation threshold of 0.37% compared to 9.7% in the initial LDPE/PS/PEBA blend where PEBA is the inside or core phase. To the best of our knowledge, this is the lowest value ever reported in the literature for a conductive polymer in melt blended systems.