  We study the Two-Higgs-Doublet Model with the aligned Yukawa sector (A2HDM)
in light of the observed excess measured in the muon anomalous magnetic moment.
We take into account the existing theoretical and experimental constraints with
up-to-date values and demonstrate that a phenomenologically interesting region
of parameter space exists. With a detailed parameter scan, we show a much
larger region of viable parameter space in this model beyond the limiting case
Type X 2HDM as obtained before. It features the existence of light scalar
states with masses $3$ GeV $\lesssim m_H^{} \lesssim 50$ GeV, or $\ 10$ GeV
$\lesssim m_A^{} \lesssim 130$ GeV, with enhanced couplings to tau leptons. The
charged Higgs boson is typically heavier, with $200$ GeV $ \lesssim m^{}_{H^+}
\lesssim 630$ GeV. The surviving parameter space is forced into the
CP-conserving limit by EDM constraints. Some Standard Model observables may be
significantly modified, including a possible new decay mode of the SM-like
Higgs boson to four taus. We comment on future measurements and direct searches
for those effects at the LHC as tests of the model.
