Visual data stories can effectively convey insights from data, yet their creation often necessitates intricate data exploration, insight discovery, narrative organization, and customization to meet the communication objectives of the storyteller. Existing automated data storytelling techniques, however, tend to overlook the importance of user customization during the data story authoring process, limiting the system’s ability to create tailored narratives that reflect the user’s intentions. We present a novel data story generation workflow that leverages adaptive machine-guided elicitation of user feedback to customize the story. Our approach employs an adaptive plug-in module for existing story generation systems, which incorporates user feedback through interactive questioning based on the conversation history and dataset. This adaptability refines the system’s understanding of the user’s intentions, ensuring the final narrative aligns with their goals. We demonstrate the feasibility of our approach through the implementation of an interactive prototype: Socrates. Through a quantitative user study with 18 participants that compares our method to a state-of-the-art data story generation algorithm, we show that Socrates produces more relevant stories with a larger overlap of insights compared to human-generated stories. We also demonstrate the usability of Socrates via interviews with three data analysts and highlight areas of future work.