Research on the agency of advanced artificial intelligence (AI) systems focuses on agency as a normative concept and on the agency of particularly agentic AI systems. While recent work also focuses on the different profiles of agentic systems, no framework exists to address the question of the type of agency instantiated by advanced AI systems, particularly when considering non-moral forms of agency. Based on established theoretical positions in philosophy, ethics, legal theory and sociology, we develop a typology of agency for frontier AI systems consisting of three dimensions: the nature of agency (moral or legal), its mode (individual or collective) and its locus (human or non-human). Combining these dimensions produces eight possible instantiations of agency, which we classify as conventional, contested or controversial. The typology separates legal from moral agency and thereby creates conceptual space for considering individual, legal, non-human agency without presupposing that advanced AI systems are moral agents. We argue that this distinction is increasingly relevant where instrumental goal pursuit complicates the attribution of AI actions to particular human actors.