Invader success and ecosystem impact are both expected to be largely driven by the functional trait distinctiveness of the resident species relative to the invaded communities. To understand the importance of trait distinctiveness for plant invasions, and the native community's trait response to the invasion, it is key to measure multiple traits simultaneously, and to incorporate intraspecific trait variation. Here we explored multidimensional patterns of inter‐ and intraspecific trait variation during the invasion of two functionally contrasting species. We constructed multidimensional trait hypervolumes for the invaders, their invaded communities, and uninvaded reference communities. The functional distinctiveness hypothesis predicts that invaders will occupy a mostly unique part of the trait hypervolume and that invasion will shift the trait composition of the native community to minimize trait overlap with the invader. Impatiens glandulifera was characterized by acquisitive traits, while Rosa rugosa had more resource conservative traits, reflecting their respective invaded habitats. Both invaders showed relatively little hypervolume overlap with the uninvaded communities, although this overlap was higher for R. rugosa (31.9%) than for I. glandulifera (14.3%). Both invaders affected community traits, mainly due to intraspecific trait changes of the resident species. As expected, invasion by R. rugosa reduced trait overlap between invader and community to 18.3%. Invasion by I. glandulifera, however, resulted in an increased trait overlap to 26.7%. In both cases the community traits shifted towards a more resource acquisitive strategy following invasion, irrespective of the invader's trait composition. This suggests that invasion‐driven community‐level intraspecific trait shifts are likely caused by increased competition for light under the invader, rather than by niche overlap. These, at first sight contradictory, results demonstrate the need for better trait‐based invasion and community ecology theory. Our results furthermore show that invaders can shift the trait occupancy of resident communities.