Hosts shifts are more likely to occur between related host species and often rely on the pathogen evolving adaptations that increase their fitness in the novel host. We investigated how viruses evolve in different host species, by experimentally evolving replicate lineages of an RNA virus in 19 different host species that shared a common ancestor 40 million years ago. We then deep sequenced the genomes of these viruses to examine the genetic changes that have occurred in different host species that vary in their relatedness. We found that parallel mutations – that are indicative of selection – were significantly more likely to occur within viral lineages from the same host, and between viruses evolved in closely related species. This suggests that a mutation that may adapt a virus to a given host, may also adapt it to closely related host species.