The Doctor is a time traveling alien who works to try and make the universe a better place. When he's critically injured, he regenerates into a new form, his personality completely changing. Some time after his twelfth incarnation, he regenerates into a complete monster, a dangerous being calling himself The Valeyard. The Valeyard haunts his own past self, trying to make right the damage he did to the universe throughout his life, and during the time war.
I'd like to run a game focusing on the adventures of the Valeyard, and the abusive relationships he has with his companions. The Doctor is quite accommodating and asexual towards his companions, but the Valeyard is the opposite; a domineering monster who takes his slaves across time and space, teaching them new torments and heights of degradation.
Possible characters for the game:
The Valeyard: Ruthlessly intelligent, boundlessly cruel, and over 900 years old, the Valeyard is every dark emotion the Doctor ever had boiled into a ruthless monster. The Valeyard is male, but the specifics of his appearance are up to personal taste. Bisexual would be ideal, but heterosexual is fine too. The Valeyard is skilled in many exotic forms of martial arts and mind control techniques, and can access gadgets and artifacts from any point in time and space. Because of how active the character will be in the game, it may be a good idea to give him multiple personalities, and have the personalities played by different players.
The Valeyard's companions: Most likely, the Valeyard has one primary female companion and a number of secondary companions. His female companion is probably a fairly normal girl from some point in Earth's history, while his secondary companions tend to be more exotic. A Dalek and/or Cyberman would both be possibilities, as could be any number of foes from the Doctor's past, up to and including The Master. (the Doctor's best friend as a child, who became an even worse rogue from timelord society than the Doctor and regenerated himself a truly insane number of times. The two have a certain degree of sexual tension.)
The Doctor: This is a fairly optional character, and the usual suspects to appear in the game would be the doctor's first, 4th, 10th, or 11th incarnations. The doctor is the yin to the Valeyard's yang, and the fact that they're the same person creates some paradoxical ramifications. Only the 11th doctor is likely at all to have sex with his companions, and that's really only because the TV series about him hasn't aired yet. (the 10th doctor came close, but he was simply too busy saving the universe) On the other hand, raping the doctor might just be a fun plan for the Valeyard to fall back on. (even if he felt the need to use some kind of alien technology to turn himself or the doctor into a female or a tentacle monster before getting down to the nasty)
The Doctor's companions: If the Valeyard attacks the doctor, it's a fair bet that the timelines of his companions will also come under attack. Rose Tyler in particular, as one of the Doctor's only companions that he loved, and who eventually gains incredible power as the Bad Wolf entity, would make an excellent plot for the Valeyard.
Depending on the preferences of the players, I can run the game either freeform or using the newly released Dr. Who RPG rules. The system is a simple, rules light system that's good for resolving mind control attempts and chases and such. (although with an understanding of how scenes will play out between players, it may be unnecessary)