The challenge I propose is to make the trajectory of one of the actors who played the Doctor (including some non-canons like Scream of the Shalka, 1960s Movies, Curse of Fatal Death, etc.) to be, somehow, elected PM with PoDs after 1963.
[PS: Bonus for whoever does the 'Doctor-PM' after the actor interprets the Doctor]
[PS2: The actors who performed the Master are also included]