Accurate requirement discovery remains a central challenge in interactive system design because users often express concrete solutions rather than the latent needs that should guide design. Semi-structured interviews can reveal these latent needs, but they are difficult for human designers to conduct at scale, while monolithic large language model (LLM) interviewers may struggle in long conversations to maintain interview structure, detect vague responses, and balance analytical control with empathic interaction. We propose a methodology-aligned multi-agent framework for AI-supported semi-structured requirement discovery. The framework separates planning, interpretation, dialogue control, and user-facing expression, allowing interview decisions and conversational delivery to be coordinated without collapsing them into a single generation loop. A dual-track evaluation, combining a simulation track against a monolithic LLM baseline with a human track involving academic researchers, suggests that this design improves structural adherence, clarification behavior, terminology reuse, and requirement-evidence extraction while remaining usable in human research contexts. These findings indicate that multi-agent design can support more scalable requirement-discovery interviews while making the interview process easier to inspect, but careful calibration is required before human-facing deployment.