Thank you, Jessica!You can mention the same story if you think it is equally as relevant to the different firms - I don't see the harm in repeating it as the firms wouldn't know you have said it to other firms (whether in an application or interview).
However, I would encourage people to not be over-reliant on one story. Even in one interview, you could easily be asked about multiple stories/subjects, and so I think it is worthwhile having a few to hand, particularly over the course of a recruitment cycle across multiple firms.