One of the core challenges presented by ascriptions of moral responsibility to corporations is to identify who or what is being held responsible. A significant source of controversy in attempts to answer this challenge is whether or not responsibility can fall on a ‘corporate entity’ distinct from the individuals that make it up. In this article I argue that both sides of this debate have incorrectly assumed that the possession of moral agency is a necessary condition for holding moral responsibility. I go on to argue that it is sufficient for a corporate entity to be a ‘morally significant system’, that is a non-agential system created by moral agents, and I develop an account of such systems. I conclude by setting out the implications of this analysis for our practices of holding corporations morally responsible.