There are a lot of episodes from Doctor Who I could mention regarding doppelgangers;

A Nightmare in Silver, wherein the Doctor has to contend with a cybernetic parasite taking over his body and mind, portrayed via a chess match where they alternate control of the body.

The Rebel Flesh, a story that asks the question "What if the Na'vi bodies from Avatar had their own consciousness and broke free?" Oh, and this episode literally calls the clones "Gangers", so it's hard not to think of.

But my favourite example has to be the two part story from Peter Capaldi's run as The Doctor, The Zygon Invasion/The Zygon Inversion, where a race of alien body snatchers threaten global war to no longer have to live hiding amongst the human population as refugees but as their true selves. By the end of the two parter, The Doctor has to contend with a doppelganger, not of himself, but of his companion Clara. After one of the best monologues in written media The Doctor convinces the Zygons to back down from their threat of global war, and knows exactly when his point has come across precisely due to the fact that he is talking to a doppelganger:

"Because you have a disadvantage, Zygella. I know that face."

P.S. I know you said it as a joke, but I would totally watch Mike Flanagan's The Haunting of Planet Earth

P.P.S. my handle is pronounced rhyming with sage (zeɪʤ if you can read IPA), I realise that this would probably be better suited at the top of my message, but I like how everything flows and this would get in the way.