The goal of music alignment is to map each temporal position in one version of a piece of music to the corresponding positions in other versions of the same piece. Despite considerable improvements in recent years, state-of-the-art methods still often fail to identify a correct alignment if versions differ substantially with respect to acoustic conditions or musical interpretation. To increase the robustness for these cases, we exploit in this work the availability of multiple versions of the piece to be aligned. By processing these jointly, we can supply the alignment process with additional examples of how a section might be interpreted or which acoustic conditions may arise. This way, we can use alignment information between two versions transitively to stabilize the alignment with a third version. Extending our previous work , we present two such joint alignment methods, progressive alignment and probabilistic profile, and discuss their fundamental differences and similarities on an algorithmic level. Our systematic experiments using 376 recordings of 9 pieces demonstrate that both methods can indeed improve the alignment accuracy and robustness over comparable pairwise methods. Further, we provide an in-depth analysis of the behavior of both joint alignment methods, studying the influence of parameters such as the number of performances available, comparing their computational costs, and investigating further strategies to increase both.