Enterprise Architecture (EA) is a consulting practice and discipline intended to improve the management and functioning of complex organizations. The various approaches to EA can be classified by how they define what is to be architected and what, as a result, is the relevant environment. Traditionally, management has been understood as “Planning, Organizing, Command, Coordinating, and Controlling” (POCCC), that is, the role is bounded within the organization. The corresponding EA approach suggests architecting IT systems to support management, with the implicit environment being members of the organization as well as partner organizations. As the objective of EA practice expands to include organizational members, technical systems, and a wider set of stakeholders, so too does the complexity it must address. This results in an enlarged domain of issues and concerns. Finally, if the objective of EA is a sustainable enterprise, then physical, societal, and ecological environments radically increase the complexity of actualizing this goal. Corresponding to this increase in scope is a parallel shift in the scope of management concerns. With the goal of pushing EA towards concerns regarding enterprise sustainability, an open socio-technical system design perspective of EA, which we have named Enterprise-in-Environment Adaptation (EiEA), is discussed. EiEA offers a comprehensive approach to respond to the demands for complexity management that arise when working towards enterprise sustainability; yet, it requires that organisations also embrace deep culture changes, such as participative design, worker empowerment, as well as shared accountability and responsibility, to name a few.