OTL the American founding fathers were influenced by a variety of classical sources (as well as more contemporary ones such as Paoli's Corsica) in drawing up their republican constitution. As we know, OTL produced a system with a single elected chief executive, the President. However, a few years later in Revolutionary France, their French counterparts decided to implement a system of multiple Roman-style consuls in order to act as checks on each others' power. What if the Americans, a little earlier, had also opted for this?
The Roman system includes the option for the consuls to appoint a temporary dictator, who has the power to override the entire judiciary and possesses supreme military command, as well as being absolved of all responsibility for any legal transgressions committed during his term in power (which the Romans limited to a maximum of six months). This would only be resorted to in times of great trial, when the fate of the republic was at stake and argument was not an option. In theory at least, the dictator could only be either a serving or former consul himself.
We know the Americans were influenced by the Romans as well as the Athenians and others, so what if a similar (but updated) system had been implemented in the United States? Assuming all the states would agree to it, of course.