The Partial Information Decomposition (PID) framework allows us to decompose the information that multiple source variables have about a single target variable. In its 10 years of existence, PID has spawned numerous theoretical and practical tools to help us understand and analyse information processing in complex systems. However, the asymmetric role of sources and target in PID hinders its application in certain contexts, like studying information sharing in multiple processes evolving jointly over time. In this talk we present a novel extension of the PID framework to the multi-target setting, which lends itself more naturally to the analysis of multivariate dynamical systems. This new decomposition is tightly linked with Integrated Information Theory, and gives us new analysis tools as well as a richer understanding of information processing in multivariate dynamical systems.