There is no reason for anyone to have a monopoly on a specific region, ie, Byzantium (which was initially a Greek city before becoming part of the Roman Empire). Technically, both Hellas and Rome may lay claim to it even though it would fall under different time periods. Even if more than one culture was a part of a region for the same time period, I do not see why they may not take part. It would be unproductive to think otherwise, IMO.