The pairwise production of neutral Higgs bosons ( h 0 A 0 , H 0 A 0 ) 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, including the full set of contributions at order O ( α 3 ew ) together with the leading O ( α 4 ew ) terms, 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  β ∼ 1 and moderate and negative values of the relevant λ 5 parameter, wherein the radiative corrections to the Higgs-pair production cross section, σ ( e + e − → A 0 h 0 / A 0 H 0 ) , can comfortably reach | δ σ | / σ ∼ 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 (MSSM). The corrections are strongly dependent on the actual value of λ 5 as well as on the Higgs mass spectrum. Interestingly enough, the quantum effects are positive for energies around √ s ≃ 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 a few tens of femtobarn, therefore amounting to a few thousand events per 500     fb − 1 of integrated luminosity. In contrast, the corrections are negative in the highest energy range (viz. √ s ∼ 1     TeV and above). We conclude that a precise measurement of the 2H final states could carry unambiguous footprints of an extended (nonsupersymmetric) Higgs sector. Finally, to better assess the scope of these effects, we compare the exclusive pairwise production of Higgs bosons with the inclusive gauge boson fusion channels leading to 2 H + X final 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.