Alternate Rome
An Alternate Rome existed at many times, either created in alternate timelines or as natural parallel universes.
The Rani's Rome
The Roman Empire of an alternate 10 BC was created by the Rani on an alternate Earth, called Terra Nova, created by the entity known as Iam. In this alternate timeline, Rome was generating electricity, building airships and steam-driven galleys, broadcasting radio, and creating many other disturbing anachronisms. The Rani had also tried to manipulate the alternate Cleopatra's three children, but had failed. (MA: State of Change)
Magog's Rome
In another alternate Rome, Magog of the Great Old Ones was worshiped along with four other Malevilus for having lead Rome to conquer the galaxy. They later provided the alternate Romans the technology to invade other dimensions. The Fourth Doctor imprisoned Magog in an empty dimension and left this Galactic Roman Empire in capable hands. (DWM: The Iron Legion)
20th Century Rome
Investigating why the multiverse was contracting, the Sixth Doctor became stuck on a number of worlds, one being a 20th century Earth where the Roman Empire never fell. (PDA: Spiral Scratch)