Climate change, biodiversity loss, and other major social and environmental problems pose severe risks. Progress has been inadequate and scientists, global policy experts, and the general public increasingly conclude that transformational change is needed across all sectors of society in order to improve and maintain social and ecological wellbeing. At least two paths to transformation are conceivable: (1) reform of and innovation within existing societal systems (e.g., economic, legal, and governance systems); and (2) the de novo development of and migration to new and improved societal systems. This paper is the final in a three-part series of concept papers that together outline a novel science-driven research and development program aimed at the second path. It summarizes literature to build a narrative on the topic of de novo design of societal systems. The purpose is to raise issues, suggest design possibilities, and highlight directions and questions that could be explored in the context of this or any R&D program aimed at new system design. This paper does not present original research, but rather provides a synthesis of selected ideas from the literature. Following other papers in the series, a society is viewed as a superorganism and its societal systems as a cognitive architecture. Accordingly, a central goal of design is to improve the collective cognitive capacity of a society, rendering it more capable of achieving and sustainably maintaining vitality. Topics of attention, communication, self-identity, power, and influence are discussed in relation to societal cognition and system design. A prototypical societal system is described, and some design considerations are highlighted.