Imagine a UNIT era modern day AU where the Doctor discovers Facebook:
He immediately sends friend requests to everyone at UNIT. The Brigadier doesn’t really understand social media (he only uses it to keep up with family stuff) but he’s very good at clicking the delete button. The Doctor is undeterred and continues to send him friend requests.
One day the Brigadier has to tell him exasperatedly, “Doctor, you can’t publicly list your education as ‘Time Lord Academy’.”
On another occasion he has to tell him to take down the picture he posted of the First Doctor that was captioned, “And here’s me in my younger days.” “I suppose this means you’ll want me remove that photograph taken during the Omega incident that said, ‘Hanging out with myself’,” the Doctor sighs.
The Doctor tries to sound cool on the internet but doesn’t because he keeps using memes that haven’t been invented yet. No one has any idea what he’s talking about and internet-savvy Jo is perpetually embarrassed.
The Master (under a paper-thin alias) stalks the Doctor’s page and likes all his posts in the hope that the Doctor will send him a friend request and he can have the satisfaction of declining it. The Doctor ignores him, but he does get a friend request from Sergeant Benton. Somehow the thought of declining that isn’t quite as satisfying.
“No, Doctor,” the Brigadier groans one morning when he sees his Facebook feed, “you cannot post… selfies… with a Dalek.” “Well if you don’t like mine, “ the Doctor replies, “just wait until you see Jo’s.”