Extreme event attribution answers the question of whether and by how much anthropogenic climate change has contributed to the occurrence or magnitude of an extreme weather event. It is also used to link extreme event impacts to climate change. Impacts, however, are often related to multiple compounding climate drivers. Because extreme event attribution typically focuses on univariate assessments, these assessments might only provide a partial answer to the question of anthropogenic influence to a high-impact event. We present a theoretical extension to classical extreme event attribution for certain types of compound events. Based on synthetic data, we illustrate how the bivariate fraction of attributable risk (FAR) differs from the univariate FAR depending on the extremeness of the event as well as the trends in and dependence between the contributing variables. Overall, the bivariate FAR is similar in magnitude or smaller than the univariate FAR if the trend in the second variable is comparably weak and the dependence between both variables is moderate or high, a typical situation for temporally co-occurring heat waves and droughts. If both variables have similarly large trends or the dependence between both variables is weak, bivariate FARs are larger and are likely to provide a more adequate quantification of the anthropogenic influence. Using multiple climate model large ensembles, we apply the framework to two case studies, a recent sequence of hot and dry years in the Western Cape region of South Africa and two spatially co-occurring droughts in crop-producing regions in South Africa and Lesotho.