The preferred channel for the search for new heavy spin-1 particles is the Drell-Yan di-lepton production, and traditionally, these searches have exploited the Narrow Width Approximation (NWA) for the signal, thereby neglecting the effect of the interference between the additional Z'-bosons and the Standard Model Z and photon. Recently, it has been established that both finite width and interference effects can be dealt with in experimental searches while still retaining the model independent approach ensured by the NWA. This assessment has been made for the case of popular single Z'-boson models currently probed at the CERN Large Hadron Collider (LHC). In this talk, we explore the phenomenology of multi Z'-boson models in relation to the scope of the CERN machine in relation to the above issues. In particular, we consider Non-Universal Extra Dimensional (NUED) scenarios and the 4-Dimensional Composite Higgs Model (4DCHM), both predicting a multi-Z' peaking structure. We conclude that in a variety of cases traditional search approaches based on the assumption of rather narrow and isolated objects might require suitable modifications to extract the underlying dynamics.