  We consider the general Three-Higgs Doublet Model (3HDM) and identify all
limits that lead to exact SM alignment. After discussing the underlying
symmetries that can naturally enforce such an alignment, we focus on the most
economic setting, called here the Maximally Symmetric Three-Higgs Doublet Model
(MS-3HDM). The potential of the MS-3HDM obeys an $\mathrm{Sp(6)}$ symmetry,
softly broken by bilinear masses and explicitly by hypercharge and Yukawa
couplings through renormalisation-group effects, whilst the theory allows for
quartic coupling unification up to the Planck scale. Besides the two ratios of
vacuum expectation values, $\tan\beta_{1,2}$, the MS-3HDM is predominantly
governed by only three input parameters: the masses of the two charged Higgs
bosons, $M_{h_{1,2}^{\pm}}$, and their mixing angle $\sigma$. Most remarkably,
with these input parameters, we obtain definite predictions for the entire
scalar mass spectrum of the theory, as well as for the SM-like Higgs-boson
couplings to the gauge bosons and fermions. The predicted deviations of these
couplings from their SM values might be probed at future precision high-energy
colliders. The new phenomenological aspects of the MS-3HDM with respect to the
earlier studied MS-2HDM are discussed.
