Normal morphogenesis depends on location-specific behaviours of cells. There are circumstances in the embryo where it would be advantageous for cells to be flexible in establishing their fate, such as in the limb bud where some cells cross between Homeobox (Hox) expression domains. It is not known how flexible cell fate determination is in the embryonic limb bud, nor is the sequence and timing of this process clear. By transposing small groups of dye and genetically labelled limb bud cells in cultured mouse embryos, we show that mesenchymal cells are capable of altering their expression of Hox genes to match that of their local environment in response to instructive mesenchymal cues. Plasticity of Hox expression wanes during embryogenesis, and is lost earlier in the proximal limb bud than distally. These findings are consistent with a model of progressive fate determination in a zone that encompasses the entirety of the limb bud mesenchyme, and suggest a mechanism for the maintenance of sharp Hox boundaries despite cell transit across them.