How could a post colonial state (like any of the nations in the Americas) be so Classical-influenced that it takes the form of a neo-Roman Republic (or perhaps Empire)? Preferably, they should brand their nation as a new Roman Republic, but if not, they can "merely" have most government and military titles Latin and most government buildings in Greco-Roman style.
Could Latin be partially adopted as a vernacular? The purpose might be to differentiate this post colonial state from its motherland and to not pick a side among different indigenous tribes or internal settler groups.