Large music content libraries often comprise multiple versions of a piece of music. To establish a link between different versions, automatic music alignment methods map each position in one version to a corresponding position in another version. Due to the leeway in interpreting a piece, any two versions can differ significantly, for example, in terms of local tempo, articulation, or playing style. For a given pair of versions, these differences can be significant such that even state-of-the-art methods fail to identify a correct alignment. In this paper, we present a novel method that increases the robustness for difficult to align cases. Instead of aligning only pairs of versions as done in previous methods, our method aligns multiple versions in a joint manner. This way, the alignment can be computed by comparing each version not only with one but with several versions, which stabilizes the comparison and leads to an increase in alignment robustness. Using recordings from the Mazurka Project, the alignment error for our proposed method was 14% lower on average compared to a state-of-the-art method, with significantly less outliers (standard deviation 53% lower).