  The fundamental description of nature, beyond the Standard Model (SM), may
include heavy neutrinos that mix and thus allow processes in which lepton
flavor is not preserved. We investigate the impact of charged currents that
couple heavy gauge bosons to heavy neutrinos and SM leptons on
lepton-flavor-violating decays of SM leptons into three charged leptons, with
no final-state neutrinos. We implement our expressions for the leading
contributions to ${\rm Br}(l_\alpha\to l_\beta\,l_\sigma\,l_\sigma)$, which
hold for either Dirac or Majorana neutrinos, to the trilepton decay $\mu\to3e$,
of the muon, and so determine sets of masses of heavy neutrinos and the heavy
gauge boson, within GeVs to few TeVs, that are consistent with the upper bounds
provided by the SINDRUM Collaboration. We find, however, that constraints
dictated by the upper bound on ${\rm Br}(\mu\to e\gamma)$, from the MEG
Collaboration, are more stringent. We utilize such parameters to find that the
contributions to tau decays are $\sim10^{-15}-10^{-13}$, well below bounds from
$B$ factories. The mixing of heavy and SM charged bosons is also investigated.
We find that current experimental data from MEG and SINDRUM would allow mixing
angles as large as $\sim10^{-2}$, for a relatively light new charged boson, but
the expected sensitivity of the Mu3e experiment would be capable of setting an
upper bound on this angle as small as $\sim10^{-4}$ if the mass of this boson
is within the range of few TeVs.
