Many models for physics beyond the Standard Model predict lepton-flavour violating decays of charged leptons at a level which may become observable very soon. We investigate the decays of a τ -lepton into three charged leptons (τ → ```′, `(′ = e, μ) in a generic way. Using effective-field-theory methods, the relevant operators are classified according to their chirality structure. For each case, we work out the Dalitz plots for the decay distributions, including interference terms which arise from four-lepton operators and radiatively induced processes. We discuss phenomenological implications, in particular the potential to distinguish different new physics models.