  It is widely believed that extensions of the minimal Higgs sector is one of
the promising directions for resolving many puzzles beyond the Standard Model
(SM). In this work, we study the unitarity bounds on the models by extending
the two-Higgs-doublet model with an additional real or complex Higgs triplet
scalar. By noting that the SM gauge symmetries $SU(2)_L\times U(1)_Y$ are
recovered at high energies, we can classify the two-body scattering states by
decomposing the direct product of two scalar multiplets into their direct sum
of irreducible representations of electroweak gauge groups. In such state
bases, the s-wave amplitudes of two-body scalar scatterings can be written in
the form of block-diagonalized scattering matrices. Then the application of the
perturbative unitarity conditions on the eigenvalues of scattering matrices
leads to the analytic constraints on the model parameters. Finally, we
numerically investigate the complex triplet scalar extension of the
two-Higgs-doublet model, finding that the perturbative unitarity places useful
stringent bounds on the model parameter space.
