  The rich vacuum structure of multi-Higgs extensions of the Standard Model
(SM) may have interesting cosmological implications for the electroweak phase
transition (EWPT). As an important example of such class of models, we consider
a particularly simple low-energy SM-like limit of a recently proposed
Grand-Unified Trinification model with the scalar sector composed of two Higgs
doublets and a complex singlet and with a global $\mathrm{U}(1)$ family
symmetry. The fermion sector of this model is extended with a family of
vector-like quarks which enhances CP violation. With the current study, we aim
at exploring the generic vacuum structure and uncovering the features of the
EWPT in this model relevant for cosmology. We show the existence of different
phase transition patterns providing strong departure from thermal equilibrium.
Most of these observations are not specific to the considered model and may
generically be expected in other multi-Higgs extensions of the SM.
