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 for the Rani on an alternate Earth, called Terra Nova by the entity known as Iam. In this alternate timeline, Rome generated electricity, built airships and steam-driven galleys, broadcast radio, and had many other disturbing anachronisms. The Rani also tried to manipulate the alternate Cleopatra's three children, but failed. (MA: State of Change)

Magog's Rome
In another alternate Rome, Magog of the Great Old Ones and four other Malevilus were worshipped for having led Rome in conquest of 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 several worlds,. One was a 20th century Earth where the Roman Empire never fell. (PDA: Spiral Scratch)