In this article, we develop a method that uses altmetric data to analyse researchers' interactions, as a way of mapping the contexts of potential societal impact. In the face of an increasing policy demand for quantitative methodologies to assess societal impact, social media data (altmetrics) have been presented as a potential method to capture broader forms of impact. However, current altmetric indicators were extrapolated from traditional citation approaches and are seen as problematic for assessing societal impact. In contrast, established qualitative methodologies for societal impact assessment are based on interaction approaches. These argue that assessment should focus on mapping the contexts in which engagement among researchers and stakeholders takes place, as a means to understand the pathways to societal impact. Following these approaches, we propose to shift the use of altmetric data towards network analysis of researchers and stakeholders. We carry out two case studies, analysing researchers' networks with Twitter data. The comparison illustrates the potential of Twitter networks to capture disparate degrees of policy engagement. We propose that this mapping method can be used as an input within broader methodologies in case studies of societal impact assessment.