There are many different forms of narrative analysis, and I believe that most of them would allow for the use of data from a single individual. As always, the key issue would be the contribution to knowledge in your field.
I’d recommend watching a TED talk by the Nigerian author - Chimamanda Ngozi Adichie - where she speaks of the dangers of ’the single story’. we are storytellers and our identities could be seen as a narrative but beware of the single story! Get on YouTube!! 😊
Wouldn't it depend on which area you are working in? In my field it is imperative to adhere to an individual's story. In other fields compiling data from many stories would be appropriate.