The techno-moral scenarios (TMS) approach has been developed to explore the interplay between technology, society and morality. Focused on new and emerging sciences and technologies, techno-moral scenarios can be used to inform and enhance public deliberation on the desirability of socio-technical trajectories. The article presents an attempt to hybridise this scenario tool, complementing the focus on ethics with an explicit acknowledgement of the multiple meanings of responsibility and of the plurality of its regimes, i.e. the institutional arrangements presiding over the assumption and assignment of responsibilities. We call this integrated technique ‘rTMS’ to stress the continuity with the original technique and, at the same time, to highlight the additional element we aim to develop: responsibility. The article describes this approach and illustrates a loosely standardised procedure that can be used to organise and conduct public engagement workshops based on rTMS.