Accumulating hints for flavor-violating Higgs bosons at the electroweak scale

We show that supplementing the Standard Model by only a second Higgs doublet, a combined explanation of $h\to e\tau$, $h\to \mu \tau$, $b\to s{\ell }^{+}{\ell }^{-}$, the $W$ mass and $R\left(D^{(*)}\right)$ as well as the excess in $t\to b{H}^{+}\left(130\mathrm{GeV}\right)\to b\overline{b}c$ is possible. While this requires flavor violating couplings, the stringent bounds from, e.g., $\mu \to e\gamma$, $\tau \to \mu \gamma$, $B_s-{\overline{B}}_s$ mixing, $b\to s\gamma$, low mass dijet, and $pp\to H^{+}{H}^{-}\to {\tau }^{+}{\tau }^{-}\nu \overline{\nu }$ searches can be avoided. However, the model is very constrained; it inevitably predicts a shift in the SM Higgs coupling strength to tau leptons as well as a nonzero $t\to hc$ rate, as indeed preferred by recent measurements. We study three benchmark points providing such a simultaneous explanation and calculate their predictions, including collider signatures which can be tested with upcoming LHC run-3 data.