  We present a one-loop analysis of the pairwise production of neutral Higgs
bosons (h0A0, H0A0) at linear colliders, such as the ILC and CLIC, within the
general Two-Higgs-Doublet Model (2HDM). We single out sizable radiative
corrections, which can well reach the level of 50 % and may be either positive
(typically for \sqrt{s} \sim 0.5 TeV) and negative (for \sqrt{s} of 1 TeV and
above). These large quantum effects, obtained in full agreement with the
current phenomenological bounds and the stringent theoretical constraints on
the parameter space of the model, can be traced back to the enhancement
capabilities of the triple-Higgs self-interactions -- a trademark feature of
the 2HDM, with no counterpart in e.g. the Minimal Supersymmetric Standard
Model. In the most favorable scenarios, the Higgs-pair cross sections may be
boosted up to barely 30 fb at the fiducial center-of-mass energy of 500 GeV --
amounting to a few thousand events per 500 inverse femtobarn of integrated
luminosity. We also compare these results with several complementary double and
triple Higgs-boson production mechanisms at order \alpha^3_{ew} and leading
\alpha^4_{ew}, and we spotlight a plethora of potentially distinctive
signatures of a Two-Higgs-Doublet structure of non-supersymmetric nature.
