Truth-finding is the fundamental technique for corroborating reports from multiple sources in both data integration and collective intelligent applications. Traditional truthfinding methods assume a single true value for each data item and therefore cannot deal will multiple true values (i.e., the multi-truth-finding problem). So far, the existing approaches handle the multi-truth-finding problem in the same way as the single-truth-finding problems. Unfortunately, the multi-truth-finding problem has its unique features, such as the involvement of sets of values in claims, different implications of inter-value mutual exclusion, and larger source profiles. Considering these features could provide new opportunities for obtaining more accurate truthfinding results. Based on this insight, we propose an integrated Bayesian approach to the multi-truth-finding problem, by taking these features into account. To improve the truth-finding efficiency, we reformulate the multi-truthfinding problem model based on the mappings between sources and (sets of) values. New mutual exclusive relations are defined to reflect the possible co-existence of multiple true values. A finer-grained copy detection method is also proposed to deal with sources with large profiles. The experimental results on three real-world datasets show the effectiveness of our approach.