The classical approach to predicting the geographical extent of species invasions consists of training models in the native range and projecting them in distinct, potentially invasible areas. However, recent studies have demonstrated that this approach could be hampered by a change of the realized climatic niche, allowing invasive species to spread into habitats in the invaded ranges that are climatically distinct from those occupied in the native range. We propose an alternative approach that involves fitting models with pooled data from all ranges. We show that this pooled approach improves prediction of the extent of invasion of spotted knapweed (Centaurea maculosa) in North America on models based solely on the European native range. Furthermore, it performs equally well on models based on the invaded range, while ensuring the inclusion of areas with similar climate to the European niche, where the species is likely to spread further. We then compare projections from these models for 2080 under a severe climate warming scenario. Projections from the pooled models show fewer areas of intermediate climatic suitability than projections from the native or invaded range models, suggesting a better consensus among modelling techniques and reduced uncertainty.