Searches for Z' bosons are most sensitive in the dilepton channels at hadron
colliders. Whilst finite width and interference effects do affect the
modifications the presence of BSM physics makes to Standard Model (SM)
contributions, generic searches are often designed to minimize these. The
experimental approach adopted works well in the case of popular models that
predict a single and narrow Z' boson allowing these effects to effectively be
neglected. Conversely, finite width and interference effects may have to be
taken into account in experimental analyses when such Z' states are wide or
where several states are predicted. We explore the consequences of these
effects in the 4-Dimensional Composite Higgs Model (4DCHM) which includes
multiple new Z' bosons and where the decays of these resonances to non-SM
fermions can result in large widths