The Aquilad by Somtow Sucharitkul is, strictly speaking, another alt-history "Rome never fell" story. But it does feature Romans zooming around on flying saucers, so it's also a star-spanning Rome tale.

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Less literal-minded examples:

Star Wars sort of makes a stab at a parallel between its Republic-turned-Empire and that of Rome, but it's never really made explicit that I'm aware of.

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Babylon 5, likewise, features the Centauri Republic, an empire which some have suggested is modeled on the Roman Empire.

Hunted, a novel by Canadian author James Alan Gardner, takes place in the 25th century, when humans have formed a super-advanced society called the Technocracy, which one character asserts is "lazy and venal, like Imperial Rome at its most decadent." (Of course, science fiction is full of depictions of empires that have gone soft. But it's not worth including them unless they're either modeled on Rome, or make the comparison explicitly.)

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Additional reporting by Alasdair Wilkins.