  We propose a search at Mu3e for lepton flavor violating axion(-like)
particles in $\mu\to 3e + a$ decays. By requiring an additional $e^+e^-$ pair
from internal conversion, one can circumvent the calibration challenges which
plague the $\mu \to e+a$ channel for axions lighter than 20 MeV. Crucially, the
corresponding reduction in signal rate is to a large extent compensated for by
Mu3e's ability to resolve highly collimated tracks. For phase I of Mu3e, we
project a sensitivity to decay constants as high as $6\times 10^9$ GeV which
probes uncharted parameter space in scenarios of axion dark matter. The
sensitivity to axions which couple primarily to right-handed leptons can be
further improved by leveraging the polarisation of the muon beam.
