  The Drell-Yan di-lepton production at hadron colliders is by far the
preferred channel to search for new heavy spin-1 particles. Traditionally, such
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 {\gamma}. 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 paper, we test the scope of the CERN machine in relation to the
above issues for some benchmark multi Z'-boson models. 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, specifically those in which the leptonic
decays modes of one or more of the heavy neutral gauge bosons are suppressed
and/or significant interference effects exist between these or with the
background, especially present when their decay widths are significant,
traditional search approaches based on the assumption of rather narrow and
isolated objects might require suitable modifications to extract the underlying
dynamics.
