People already do it with chain-of-thought and you could get away with a few dozen examples if you wanted to try this.
Just uploaded the examples as-is to OpenAI, selected 3.5 as the model to fine-tune and about 20 minutes later I had my model.
Works fine, asks good questions, can ask more than 1 follow up question if needed, and actually changes its answers based on the clarifying questions.
https://imgur.com/a/SsXunVN