Rome and Carthage were ruled by elected diarchs. Sparta had two kings, and the Seleucids and Ptolemies were frequently ruled by father-son co-regencies, too. Not to mention other official positions: at one point, there were twenty Quaestors (not just two) and sixteen Praetors (not just one). It's pretty safe to say that these characters exist (in a roleplaying sense); the game just doesn't show them.
However, the problem with republics having two rulers elected every year is that the game will burn through characters at a ridiculous pace. The number of characters shown by the game at any time in no way reflects how many aristocrats were alive at that time; having two rulers will mean that either more characters will need to be represented, or the game will have to "retire" characters far more frequently. I know this, because once upon a time I modded my game to allow it. It worked really well for a decade or two, but after a while you
Personally, I always mod the game so that consuls (and suffets) rule for only one year rather than two, and just assume that the second co-ruler is there, but more in the "background" as it were.