The frequency of evolutionary biome shifts during diversification has important implications for our ability to explain geographic patterns of plant diversity. Recent studies present several examples of biome shifts, but whether frequencies of biome shifts closely reflect geographic proximity or environmental similarity of biomes remains poorly known. We explore this question by using phylogenomic methods to estimate the phylogeny of Hakea, a diverse Australian genus occupying a wide range of biomes. Model-based estimation of ancestral regions indicates that Hakea began diversifying in the Mediterranean biome of southern Australia in the Middle Eocene – Early Oligocene, and dispersed repeatedly into other biomes across the continent. We infer around 47 shifts between biomes. Frequencies of shifts between pairs of biomes are usually similar to those expected from their geographic connectedness or climatic similarity, but in some cases are substantially higher or lower than expected, perhaps reflecting how readily key physiological traits can be modified to adapt lineages to new environments. The history of frequent biome-shifting is reflected in the structure of present-day assemblages, which tend to be more phylogenetically diverse than null-model expectations. The case of Hakea demonstrates that the radiation of large plant clades across wide geographic areas need not be constrained by dispersal limitation or conserved adaptations to particular environments.