Qualitative insights from user experiences are critical for informing product and policy decisions, but scaling qualitative data collection is constrained by the availability of trained interviewers. Recent work has explored using large language models (LLMs) to automate interviewing, yet existing systems lack a principled mechanism for balancing systematic coverage of predefined topics with adaptive exploration, or the ability to pursue follow-ups, deep dives, and emergent themes that arise organically during conversation. In this work, we formulate adaptive semi-structured interviewing as an optimization problem over the interviewer's behavior. We define interview utility as a trade-off between coverage of a predefined interview topic guide, discovery of relevant emergent themes, and interview cost measured by length. Based on this formulation, we introduce SparkMe, a multi-agent LLM interviewer that performs deliberative planning via simulated conversation rollouts to select questions with high expected utility. We evaluate SparkMe through controlled experiments with LLM-based interviewees, showing that it achieves higher interview utility, improving topic guide coverage ($+4.7\%$ over the best baseline) and eliciting richer emergent insights while using fewer conversational turns than prior LLM interviewing approaches. We further validate SparkMe in a user study with $70$ participants across $7$ professions, where occupational domain experts rate it as producing higher-quality, more adaptive interviews and validate profession-specific insights not captured by the baseline. In addition, separately recruited experts in qualitative or human-centered research also find stronger responsiveness and probing in SparkMe. The code and evaluation resources for SparkMe are available as open source at https://github.com/SALT-NLP/SparkMe.

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