  Lepton flavour violating (LFV) processes are a smoking gun signal of new
physics (NP). If the semileptonic $B$ decay anomalies are indeed due to some
NP, such operators can potentially lead to LFV decays involving the second and
the third generation leptons, like $\tau\to 3\mu$. In this paper, we explore
how far the nature of NP can be unraveled at the next generation $B$-factories
like Belle-II, provided the decay $\tau\to 3\mu$ has been observed. We use four
observables with which the differentiation among NP operators may be achieved
to a high confidence level. Possible presence of multiple NP operators are also
analysed with the Optimal Observable technique. While the analysis can be
improved even further if the final state muon polarisations are measured, we
present this work as a motivational tool for the experimentalists, as well as a
template for the analysis of similar processes.
