  The pairwise production of neutral Higgs bosons is analyzed in the context of
the future linear colliders, such as the ILC and CLIC, within the general
Two-Higgs-Doublet Model (2HDM). The corresponding cross-sections are computed
at the one-loop level in full compliance with the current phenomenological
bounds and the stringent theoretical constraints inherent to the consistency of
the model. We uncover regions across the 2HDM parameter space, mainly for low
tan\beta near 1 and moderate values of the relevant lambda_5 parameter, wherein
the radiative corrections to the Higgs-pair production cross sections can
comfortably reach 50% This behavior can be traced back to the enhancement
capabilities of the trilinear Higgs self-interactions -- a trademark feature of
the 2HDM, with no counterpart in the Minimal Supersymmetric Standard Model.
Interestingly enough, the quantum effects are positive for energies around 500
GeV, thereby producing a significant enhancement in the expected number of
events precisely around the fiducial startup energy of the ILC. The Higgs-pair
production rates can be substantial, typically amounting to a few thousand
events per 500 inverse femtobarn of integrated luminosity. In contrast, the
corrections are negative in the highest energy range (1 TeV). We also compare
the exclusive pairwise production of Higgs bosons with the inclusive gauge
boson fusion channels leading to 2H+X finals states, and also with the
exclusive triple Higgs boson production. We find that these multiparticle final
states can be highly complementary in the overall Higgs bosons search strategy.
