Who chooses to step into a TARDIS and leave their life behind, potentially forever? Would you?
A different idea for a companion’s motivation from RPGnetter Shay Guy - she decides to go with the Doctor because she’s afraid. In game terms, obviously the character wouldn’t have Brave and might have to buy off Unadventurous - possibly repeatedly. But it’s certainly a good rationale for a Screamer! on the team.
So what about your companion characters? Why are they running for their lives in far-flung times and places? Is it for the hell of it, is it to see wonders, is it because of the personality of the pilot - love, perhaps, or fear for their safety?
And what criteria does the pilot have for taking people on?
And what happens when everything changes...?