Over the next week, Rosie frequently asked for Miss Hassiter to help her dress, put her to bed, read her a book, play with her, or give her a bath, instead of mom. Anytime I accedently slipped and called her "sweetie" or something else like that, she would respond, "No, be Miss Hassiter!" so in this way she defined her expectations.
At the same time, she was very caught up in her "Frozen" fandom, and would ask me to be either Anna or Elsa (or, rarely, another character), sometimes to take a part in a song.
As that faded in frequency, Rosie then asked me to either play Doc (with or without the Doc McStuffins doll in hand) or Doc's mom, when Rosie was being Doc. I've seen a lot of the show and can sometimes do a decent version of either character's voice, but in fact this is harder than being Miss Hassiter, whom I can just make up as I go.
Then Rosie watched some of Finding Nemo at a friend's house, and had a flurry of asking me to be Nemo. Nemo is active, enthusiastic, curious, and doesn't know much about the world of people, and she seemed to really enjoy being asked about things around us. She also sometimes asked to see his little "lucky" fin.
Brian got recruited to be Dori, and he really does a good job of it, so most of the time Rosie asked me to be Dori, I suggested she have dad do it, but I played that role, as well as Nemo's dad, a few times too.
This tendency to ask us to 'be' a character, has slowed down a bit for the moment, but I wanted to record it a bit before it's gone altogether. Rosie has also once asked me to be another living person, but I refused, indicating that I didn't want to misrepresent them.
As I've commented to Brian, I think, in addition to being imaginative, having us be characters also gets us to pay more attention to her, instead of being distracted by other things around us and cleaning or looking at our phones or other things that would be out of character when we're playing a part. I've tried to get better at being attentive in play whether or not I'm "being" someone, as well.
Anyway, it's been very interesting, and sometimes amusing, but sometimes we've also gotten tired of it and... almost jealous, really, wanting her to want us to be ourselves and not someone else all the time. So that could be why she's not doing it so much now.