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Data fusion, within the data integration pipeline, addresses the problem of discovering the true values of a data item when multiple sources provide different values for it. An important contribution to the solution of the problem can be given by assessing the quality of the involved sources and relying more on the values coming from trusted sources. State-of-the-art data fusion systems define source trustworthiness on the basis of the accuracy of the provided values and on the dependence on other sources, and recently it has been also recognized that the trustworthiness of the same source may vary with the domain of interest. In this paper we propose STORM, a novel domain-aware algorithm for data fusion designed for the multi-truth case, that is, when a data item can also have multiple true values. Like many other data-fusion techniques, STORM relies on Bayesian inference. However, differently from the other Bayesian approaches to the problem, it determines the trustworthiness of sources by taking into account their authority: Here, we define authoritative sources as those that have been copied by many other ones, assuming that, when source administrators decide to copy data from other sources, they choose the ones they perceive as the most reliable. To group together the values that have been recognized as variants representing the same real-world entity, STORM provides also a value-reconciliation step, thus reducing the possibility of making mistakes in the remaining part of the algorithm. The experimental results on multi-truth synthetic and real-world datasets show that STORM represents a solid step forward in data-fusion research.