  Multi-step phase transition provides a paradigm in which a broken symmetry
during phase transition can be restored, enriching the phenomena of both dark
matter and baryon asymmetry. We study the dynamics of the multi-step phase
transition in the standard model extension with additional isospin $N$-plet
scalar field $\Phi_2$ under a discrete $\mathbb{Z}_2$ symmetry. We find that
the multi-step phase transition could be triggered if there is a moderately
large coupling between the Higgs and the $\Phi_2$ and this coupling is required
to be larger as the mass of the $\Phi_2$ and/or isospin increase. The
first-order phase transition at the first (second) step can be realized by the
thermal loop (tree-level barrier) effects. Thus it is more likely that a
detectable spectrum of gravitational waves can be produced at the second step
of the phase transition.
