The emergence and evolution of engineering biology, and its potential to address multiple global challenges is associated with the rise of biofoundries. These innovation intermediaries are facilities that employ advanced automation and computational analytics to accelerate engineering biology applications. Yet, for biofoundries to fully achieve their promise of generating applications that address grand societal challenges, they need to meet three key challenges: translation of research technology and its commercialization, attention to sustainability, and responsible innovation. Using web content analysis and interviews, this paper explores the functions and capabilities undertaken by existing public biofoundries, the extent to which they address these three challenges, and opportunities and models for enhancement. We also probe the roles undertaken by three other contrasting types of innovation intermediaries to identify practices and opportunities for integration and partnering with public biofoundries. We find that public biofoundries exhibit relatively strong capabilities for research translation, whereas efforts toward sustainability and responsibility are generally less prominent. For biofoundry enhancement, we propose an organisational model based on external partnering where public biofoundries are positioned as intermediaries within regional innovation systems. The framework put forward is reproducible and could be used in other contexts for assessing innovation intermediary organisational functions and capabilities toward meeting societal challenges.