As AI-driven product development accelerates, the bottleneck is shifting from how we build to what we build. Traditional human brainstorming faces challenges including groupthink, echo chambers, and limited diversity. To address this, we present a multi-agentic architecture that simulates roundtable brainstorming through two phases: divergent thinking to generate diverse ideas, and convergent thinking to evaluate and rank the most promising ones. The system employs diverse AI personas that engage in roundtable discussions, guided by an agentic facilitator that steers the discussion toward productive outcomes. Personas maintain private thoughts while commenting publicly, with ideas emerging organically throughout the discussion. Per-persona quotas on idea submissions and votes promote balanced participation while producing natural rankings. Throughout the session, the system tracks each idea's lineage, capturing how concepts originate and cross-pollinate over time. We demonstrate this approach through a case study generating consumer ideas for AI smart glasses, showing (i) it produces diverse, relevant ideas with insights into their evolution; (ii) the cumulative exchange of perspectives across personas cultivates a shared context that progressively deepens the quality of discussion and the ideas produced.