The first step for transforming the current linear and degenerative socio-economic systems into ones that are circular and regenerative is to understand how they grow and develop. Here, we explore whether there are limits to robustness of a socio-economic system as the result of a linear metabolic structure, and how those limits could theoretically be affected by its transition to a circular economy. First, we study how the circular use of materials and the economic openness of the EU27 would affect the value of its circularity rate (as defined by Eurostat), theoretically. Then, given that the circularity rate does not capture regenerative aspects, we develop a conceptual framework based on regenerative economics and on indicators from ascendency analysis and ecological network analysis. We use this framework to assess a theoretical future case where the EU27 manages to successfully transition to a CE within its given linear material flow metabolism. The results show that there are limits to robustness, and which do not necessarily correspond to a maximum circularity rate. None of the 45 scenarios assessed can theoretically lead to the maximum robustness observed in natural ecosystems, including those which maximize the circularity rate. Interestingly, the highest possible robustness value is obtained at a circularity rate of about 33% as a combination of a material recovery rate of 30% and of a material export rate of 10%. Scenarios of higher circularity rate (as the result of higher export rates and/or higher material recovery rates) seem to lead to brittle networks. Other indicators from regenerative economics are also discussed. Furthermore, the results show that even if substantial steps are taken by the EU27 towards a circular economy, 100% circularity rate seems to be unlikely. This analysis highlights that the use of tools from regenerative economics can assist policy makers and researchers to account for and to monitor network properties such as those of resilience and robustness, during strategic planning activities for a transition to a regenerative circular economy.