  The interplay between topology and interactions on the edge of a two
dimensional topological insulator with time reversal symmetry is studied. We
consider a simple non-interacting system of three helical channels with an
inherent $\mathbb{Z}_{2}$ topological protection, and hence a zero-temperature
conductance of $G=e^2/h$. We show that when interactions are added to the
model, the ground state exhibits two different phases as function of the
interaction parameters. One of these phases is a trivial insulator at zero
temperature, as the symmetry protecting the non-interacting topological phase
is spontaneously broken. In this phase, there is zero conductance $G=0$ at
zero-temperature. The other phase displays enhanced topological properties,
with the neutral sector described by a massive version of $\mathbb{Z}_{3}$
parafermions. In this phase, the system at low energies displays an emergent
$\mathbb{Z}_3$ symmetry, which is not present in the lattice model, and has a
topologically protected zero-temperature conductance of $G=3e^2/h$. This state
is an example of a dynamically enhanced symmetry protected topological state.
