  We consider possible beyond-the-Standard-Model (BSM) effects that can
accommodate both the long-standing tension in the anomalous magnetic moment of
the muon, $a_\mu=(g-2)_\mu/2$, as well as the emerging $2.5\sigma$ deviation in
its electron counterpart, $a_e=(g-2)_e/2$. After performing an EFT analysis, we
consider BSM physics realized above the electroweak scale and find that a
simultaneous explanation becomes possible in models with chiral enhancement.
However, this requires a decoupling of the muon and electron BSM sectors to
avoid the strong constraints from $\mu\to e\gamma$. In particular, this
decoupling implies that there is no reason to expect the muon electric dipole
moment (EDM) $d_\mu$ to be correlated with the electron EDM $d_e$, avoiding the
very stringent limits for the latter. While some of the parameter space for
$d_\mu$ favored by $a_\mu$ could be tested at the $(g-2)_\mu$ experiments at
Fermilab and J-PARC, a dedicated muon EDM experiment at PSI would be able to
probe most of this region.
