  We extend the relativistic mean-field models with hadron masses and
meson-baryon coupling constants dependent on the scalar $\sigma$ field, studied
previously to incorporate $\Delta(1232)$ baryons. Available empirical
information is analyzed to put constraints on the couplings of $\Delta$s with
meson fields. Conditions for the appearance of $\Delta$s are studied. We
demonstrate that with inclusion of the $\Delta$s our equations of state
continue to fulfill majority of known empirical constraints including the
pressure-density constraint from heavy-ion collisions, the constraint on the
maximum mass of the neutron stars, the direct Urca and the gravitational-baryon
mass ratio constraints.
