  Despite their structural similarities, SrBi$_2$Ta$_2$O$_9$ (SBT) and
SrBi$_2$Nb$_2$O$_9$ (SBN) undergo a different sequence of phase transitions.
The phase diagram of SBT as a function of the temperature includes an
intermediate phase between the high-temperature phase and the ferroelectric
ground state, while in the Niobium compound the intermediate phase is
suppressed and a single transition between the high- and low temperature
structures is observed. We present \emph{ab initio} calculations that reveal
the relevance of a trilinear coupling between three symmetry-adapted modes to
stabilize the ground sate in both compounds, being this coupling much stronger
in SBN. Within the framework of the phenomenological Landau theory, it is shown
that by solely increasing the strength of the trilinear coupling the topology
of the phase diagram of SBT can change up to suppress the intermediate phase.
Monte Carlo simulations on an idealized $\phi^4$ Hamiltonian confirm that the
trilinear coupling is the key parameter that determines the sequence of phase
transitions and that for higher dimensionality of the order parameters the
stability region of the intermediate phase is narrower.
