  The SM-like Higgs pair productions are discussed in the framework of the
general CP-violating two-Higgs-doublet model, where we find the CP-violating
mixing angles can be related to the Higgs self couplings. Therefore, the future
experimental searches for Higgs boson pairs can be constrained by the improved
precision of the electric dipole moment measurements. Based on a series
constraints of the SM-like Higgs boson signal fits, the perturbative unitarity
and stability bounds to the Higgs potential, and the most recent LHC searches
for the heavy Higgs bosons, we suggest a set of benchmark models for the future
high-energy collider searches for the Higgs pair productions. The $e^+ e^-$
colliders operating at $\sqrt{s}=$ (500 GeV, 1 TeV) are capable of measuring
the Higgs cubic self couplings of the benchmark models directly. We also
estimate the cross sections of the resonance contributions to the Higgs pair
productions for the benchmark models at the future LHC and SppC/Fcc-hh runs.
