We tackle the problem of computing a consensus according to multiple ethical principles – which can include, for example, the principle of maximum freedom associated with the Benthamite doctrine and the principle of maximum fairness associated with the Rawlsian principles – among the preferences of different individuals in the context of Group Decision-Making (GDM). More formally, we put forward a novel formalisation of the above-mentioned problem based on a multi-lp-norm approximation problem that aims at minimising multiple p-metric distance functions, where each parameter p represents a given ethical principle. Our contribution incurs obvious benefits from a social-choice perspective. Firstly, our approach significantly generalises state-of-the-art approaches that were limited to only two ethical principles (p=1, for maximum freedom, and p=∞, for maximum fairness). Secondly, our experimental results considering an established test case demonstrate that our approach is capable, thanks to a novel re-weighting scheme, to compute a multi-norm consensus that takes into account each ethical principle in a balanced way, in contrast with state-of-the-art approaches that were heavily biased towards the p=1 ethical principle.