The present upper bound on $\kappa_e$, the ratio between the electron Yukawa coupling and its Standard Model (SM) value, is of ${\cal O}(600)$. We ask what would be the implications in case that $\kappa_e$ is close to this upper bound. Such enhancement will exclude the SM as a good low energy effective theory (SM-EFT), as well as two Higgs doublet models (2HDM) with natural flavor conservation (NFC). We thus focus on 2HDM without NFC. In this framework, we find the following consequences: (i) Under certain conditions, measuring $\kappa_e$ and $\kappa_V$ would be enough to predict values of Yukawa couplings for other fermions and for the $H$ and $A$ scalars. (ii) In the case that the scalar potential has a softly broken $Z_2$ symmetry, the second Higgs doublet must be light, but if there is hard breaking of the symmetry, the second Higgs doublet can be much heavier than the electroweak scale and still allow the electron Yukawa coupling to be very different from its SM value. (iii) CP should be an excellent symmetry of the scalar potential and of the Yukawa sector. (iv) LHC searches for $e^+e^-$ resonances constrain this scenario in a significant way.