Addressing the intensifying climate crisis and the transgression of multiple Planetary Boundaries requires a deep socio-ecological transformation. From the perspective of complex systems, the following question arises: Which leverage points need to be addressed to push socio-economic systems in a more sustainable direction? While we agree that the leverage points heuristic proposed by Donella Meadows is useful, we herein argue that it would benefit from emphasizing the pivotal role of socioeconomic material stocks as enablers and inhibitors of transformative change. Currently, socioeconomic stocks are pigeonholed as a shallow leverage point. However, from a socio-metabolic perspective, existing stocks are key drivers of environmental pressures, which foster unsustainable individual behaviours and thus create path dependencies and lock-ins. Stocks can even shape the societal perception of challenges that often foster unsustainable responses. Hence, system-wide socio-ecological change hinges on fundamental changes in socioeconomic stocks. Transformative change requires a reconceptualization of stocks embracing their multidimensional and cross-cutting interconnectedness with the deeper leverage points around system feedback, design, and intent. Rather than looking for the one deep leverage point, we suggest that a well-coordinated intervention strategy needs to target multiple leverage points while systematically considering socioeconomic stocks as an inherent, critical system property to be altered.