You could say there was more than one Roman Empire, but not always. As early as 253 CE, the Emperor Valerian thought the empire was too large for him to rule well.
He split it into western and eastern halves. He gave the western half to his son to rule. He kept the eastern half. When Valerian died in 260 CE, his son took over the whole empire. In 284 CE, a general named Diocletian became emperor. He also thought the empire was too large for one person to rule. He gave control of the western half to a trusted officer. When their rule failed, civil wars divided Rome. But in 324 CE, Constantine the Great, the first Christian emperor, was able to reunite the empire. In 395 CE, almost 60 years after Constantine’s death, the Roman Empire split again. The Eastern Roman Empire was based in Constantinople. The Western Roman Empire was based in Rome. This time the split was permanent.