I was thinking something like in Mass Effect or Dragon Age character creators. The backstory system would work great too; you'd be able to determine where and when you meet the Doctor, and what occupation you had. What you pick would determine what event would occur that you would help the doctor fix (like the backstory related opening quests in Dragon Age).
It could look something like this (ala Mass Effect):
Select Location: (choose a location with predetermined effects on plot, some attributes, and side quests)
Select Personal Background: (choose between brief summaries of family background that have predetermined effects on plot and side quests)
Select Occupation: (choose between occupations that affect plot, certain attributes, and side quests)
To use an example from the show: A configuration such as:
Select Location: London
Select Personal Background: Two siblings, Divorced parents, etc.
Select Occupation: Medical Intern
Would result in the game panning out like season 3.
Of course, to truly be effective, the game would have to use original plots, rather than simply reenact the show.
