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Trait intraspecific variability determines community dynamics and species coexistence. In response to competition, plants can display intraspecific variability to enhance their competitive ability or stabilise their niche differences with competitors. This response is multidimensional because it involves changes along different functional axes and inevitable trade‐offs between traits. Here, we transposed the recent concept of the multidimensional trait space to the analysis of intraspecific plant response to competition. We specifically tested the following: (a) in the absence of competitors, the plant multidimensional trait space will be packed towards strategies promoting plant colonisation; and (b) with competitors, the plant multidimensional trait space will be directed towards competition with its size and shaping characteristics dependent on competitor species richness.We studied trait intraspecific variability of two clonal species, Brachypodium pinnatum (L.) P. Beauv. and Elytrigia repens (L.) Gould, in response to competition. We analysed plant response in the absence of competitors and in competition. Competition treatments included intraspecific and interspecific experimental mixtures with increasing species richness. For each target species and each treatment, we built an hypervolume based on six traits involved in the three‐dimensional competition (i.e., ramet and connection traits). We measured these hypervolumes for their size, similarity and the contribution of traits in their shaping.In the absence of competitors and for both species, we demonstrated a multidimensional trait space packing towards a colonisation strategy. Under competition, the multidimensional trait spaces of the two target species were the widest at the extremes of the richness gradient, that is, intraspecific and interspecific high richness competition treatments. High intraspecific variability either promoted niche differentiation from individuals of similar species or reflected the large range of competitive responses deployed when plants were faced with many different competitor identities. The multidimensional response process was based on fine adjustments of various traits depending on the surrounding neighbourhood composition and more specifically, on the competitor functional similarity with the target species.This study emphasises the multidimensionality of species competitive response, and also underlines the so far neglected importance of competitor species richness for trait intraspecific variability and subsequently community assembly. A plain language summary is available for this article. Plain Language Summary [ABSTRACT FROM AUTHOR]