Low-carbon energy transitions demand long-term systemic transformations and the meaningful engagement of society. Most existing approaches to engaging society with energy and climate change fail to sufficiently address the systemic nature of this challenge, being compartmentalised and narrowly focused on discrete forms of engagement in specific parts of energy systems (e.g. behaviour change in energy demand, or public deliberation on the acceptability of low-carbon technologies). We present a novel systemic approach to societal engagement that addresses these deficiencies through two interlinked mapping methods: (i) a systematic approach to mapping diverse public engagements across energy systems; and (ii) a Distributed Deliberative Mapping (DDM) approach to the social appraisal of sustainable energy futures. We show how UK public engagement with energy is much more diverse than dominant approaches posit, broadening out to encompass society-led issue formation and actions. Attending to these more varied models of energy participation when eliciting public views in DDM further opens up public framings, values and concerns about energy futures. Our analysis reveals expert, policy-maker and public support for more distributed energy system futures that pay greater attention to the roles of society. Going beyond narrow discrete understandings of communication and public engagement towards systemic approaches to mapping participation can provide plural and robust forms of social intelligence needed to govern low-carbon energy system transitions in more socially responsive, just and responsible ways.