With accelerating rates of invasion being documented in many ecosystems, communities of interacting invasive species are becoming increasingly common. Opposing theories predict that invaders can either hinder or promote one another's success. Additionally, evidence suggests that co-occurring invaders can interact to amplify or mitigate one another's impacts on ecosystems. However, there has not been a quantitative review on interactions among multiple invasive animals. Here I use a meta-analysis approach to show that, across a global scale, the mean interaction among invaders was to reduce one another's performance. This pattern was consistent when considering interactions between marine animals but interactions were neutral overall in terrestrial and freshwater ecosystems. Crucially, individual studies showed that neutral interactions were the most common interaction type. Further, I demonstrate that the combined ecological impacts of multiple invaders were frequently the sum of their independent effects (additive) but the mean effect was non-additive and less than predicted (antagonistic). In both meta-analyses, the disparity between the most frequent and mean interaction type indicates that case studies of multiple invasions commonly have different outcomes to global trends. These results will help predict how co-occurring invasive animals interact and assist in developing management strategies for problematic invaders in our changing world.