General-purpose AI (GPAI) systems, increasingly powered by LLMs, have been introduced in an increasing number of safety-critical systems, from clinical conversational assistants to real-time decision explanations in autonomous driving. Simultaneously, safety engineers looking to use general-purpose AI systems are faced with significant challenges, such as deep complexity in the way such com-ponents are developed, which can exceed the context-specific bounds of established assurance methodologies. We appraise existing methods within the GPAI safety literature, which might help to ameliorate novel concerns. We ground our approach in the Centre for Assuring Autonomy’s BIG Argument for AI Safety Cases. By re-stating open problems across domains related to GPAI, we present relevant up-stream and downstream considerations which build on the BIG Argument for those integrating closed-source GPAI systems in safety-critical contexts.