  We present a multifrequency study of the transient $\gamma$-ray source 4FGL
J1544.3-0649, a blazar that exhibited a remarkable behaviour raising from the
state of an anonymous mid-intensity radio source, never detected at high
energies, to that of one of the brightest extreme blazars in the X-ray and
$\gamma$-ray sky. Our analysis shows that the averaged $\gamma$-ray spectrum is
well described by a powerlaw with a photon index of $1.87\pm0.04$, while the
flux above 100 MeV is $(8.0\pm0.9)\times10^{-9}\:{\rm photon\: cm^{-2}\:
s^{-1}}$, which increases during the active state of the source. The X-ray flux
and spectral slope are both highly variable, with the highest 2-10 keV flux
reaching $(1.28\pm0.05)\times10^{-10}\:{\rm erg\:cm^{-2}\:s^{-1}}$. On several
observations the X-ray spectrum hardened to the point implying as SED peak
moving to energies larger than 10 keV. As in many extreme blazars the broadband
spectral energy distribution can be described by a homogeneous one-zone
synchrotron-self-Compton leptonic model. We briefly discuss the potential
implications for high-energy multi-messenger astrophysics in case the dual
behaviour shown by 4FGL J1544.3-0649 does not represent an isolated case, but
rather a manifestation of a so far unnoticed relatively common phenomenon.
