The Eastern Roman Emperor Justinian certainly made the attempt. He was able to have his military forces crush the Vandals in modern Tunisia and recapture Carthage. He also recovered the south eastern portion of Spain from the Visogoths and fought a very long, twenty year war against Ostrogoths, recapturing most of the Italian peninsula. Unfortunately, shortly after the Ostrogoths were destroyed, the Lombards invaded Italy and overran much of the Italian peninsula. The Eastern Roman Empire were able to retain Ravenna for a long time, but they lost control of Rome rather quickly.
Sources: "A History of the Ostrogoths" by Thomas Burns
"Atlas of Medieval Europe" by Donald Matthew