I know this is a joke/meme, but I sincerely think of the Roman Empire a surprising amount of times. I find myself obsessing over how Roman citizens were living just as complex lives as we are today, or about Marcus Aurelius’ life and philosophy, or about how the Republic fell and became a totalitarian state.
Have you ever read: I, Claudius? If not, you should. Going by your description, it should really scratch that itch in a very well written way. Recommended to you by a fellow Roman Empire fanatic ^^
Edit: And to answer your question: Yes, quite often I do.
The excellent “I, Claudius” BBC TV series was repeated recently (I think it was on BBC4). One of my all time favourites. I had forgotten how funny the Caligula episode is, and the demise of Messalina is truly bone-chilling.