  Recent progress on muon $g-2$ measurement prompts one to take it even more
seriously. In the general two Higgs doublet model that allows extra Yukawa
couplings, we take a simplified approach of single enhanced coupling. We fix
the charged lepton flavor violating coupling, $\rho_{\tau\mu} =
\rho_{\mu\tau}$, via the one-loop mechanism, for illustrative masses of the
heavy scalar $H$ and pseudoscalar $A$, where we assume $m_A = m_{H^+}$. Since
extra top Yukawa couplings are plausibly the largest, we turn on $\rho_{tt}$
and find that LHC search for $gg \to H,\,A \to \tau\mu$ gives more stringent
bound than from $\tau\to \mu\gamma$ with two-loop mechanism. Turning on a
second extra top Yukawa coupling, $\rho_{tc}$, can loosen the bound on
$\rho_{tt}$, but LHC constraints can again be more stringent than from $B \to
D\mu\nu$ vs $De\nu$ universality. This means that evidence for $H,\,A \to
\tau\mu$ may yet emerge with full LHC Run 2 data, while direct search for
$\tau^\pm\mu^\mp bW^+$ or $t\bar cbW^+$ (plus conjugate) may also bear fruit.
