In rural areas, the possibility of putting up one road next to another would almost always exist.
In urban areas, there are a few possibilities. Assuming that the present road system isn't run by a single party that is bound by contract to charge a low rate (I think the most probable situation), if present roads are being run so poorly that there exists a large profit margin, it might be in someones interest to buy up existing properties or options and in fact build a road next to an existing one and start competing.
Asides from this, there is always the option of building tunnels underneath, assuming one does not meddle with the infrastructure of the other town.
Hey, this is a private residence man...