  In this work, dual electroweak phase transition (EWPT) consisting of two
phases, is carefully studied in the two-Higgs-doublet model with the $S_3$
discrete symmetry. The role of $S_3$ here is to further separate the stages of
the electroweak phase transition, compared to that of the original
two-Higgs-doublet model (2HDM). The strength of the electroweak phase
transition $(S)$ in the model under consideration is large enough for the
first-order EWPT, specifically $1 < S < 2.8$. The ratio between the two vacuum
expectation values (VEVs), $\tan\beta = v_2/v_1$, is proven to have no effects
on the strength of the phase transition. This ratio only affects the mass
domain that causes the first-order phase transition. Furthermore, in this paper
we will show clearly that when studying the EWPT in models of more than one
scalar field that generates masses, one needs to analyze the problem of phase
transition under multiple stages. In other words, the effect of the first stage
of symmetry breaking to the second one, is to simplify by suggestion that
vacuum expectation value of the Higgs boson responsible for the initial stage
is proportional to that of the field for the next stage.
