Roma III was one of many Known Worlds where the Roman Empire never fell. It differed from Roma I in that the Emperor of the Seres, Yung Lo, won the coin toss to become Emperor of the World rather than the Roman Emperor Cosimo. However, the Series decamped to Rome and quickly adopted Roman culture.
Roma III was directly "threewards" of Roma I. (PROSE: Warlords of Utopia)