How many Roman Empires were there? One? Two? None? The answer to that question depends on what year you are talking about.
As early as 253 CE, the Emperor Valerian thought the empire was too large for him to rule successfully. He divided it into western and eastern halves, and gave the western half to his son to rule, while he ruled the eastern half. When Valerian died in 260 CE, his son ruled the entire empire. In 284 CE, a general named Diocletian became emperor. He too thought the empire was too large to be ruled by one person. He gave control of the western half to a trusted officer. When their rule collapsed, civil wars again divided Rome. But in 324 CE, Constantine the Great, the first Christian emperor, managed to reunite the whole empire. In 395 CE, almost 60 years after Constantine’s death, the Roman Empire again split in two, with the Eastern Roman Empire based in Constantinople and the Western Roman Empire based in Rome. This time the division was permanent.