Genetic variation in viral structural proteins is often explained by evolutionary escape of strong host defenses through processes such as immune evasion, host switching, and tissue tropism. An understanding of the mechanisms driving evolutionary change in virus surface proteins is key to designing effective intervention strategies to disease emergence. This study investigated the predictability of virus genomic evolution in response to highly specific differences in host receptor structure. The bacteriophage PhiX174 was evolved on three E. coli mutant hosts, each differing only by a single sugar group in the lipopolysaccharides, used for phage attachment. Large phage populations were used in order to maximize the amount of sequence space explored by mutation, and thus the potential for parallel evolution. Repeatability was assessed by genome sequencing of multiple isolates from endpoint populations and by fitness of the endpoint population relative to its ancestor. Evolutionary lines showed similar magnitudes of fitness increase between treatments. Only one mutation, occurring in the internal DNA pilot protein H, was completely repeatable, and it appeared to be a necessary stepping stone toward further adaptive change. Substitutions in the surface accessible major capsid protein F appeared to be involved in capsid stability rather than specific interactions with host receptors, suggesting that non-specific alterations to capsid structure could be an important component of adaptation to novel hosts. 33% of mutations were synonymous and showed evidence of selection on codon usage. Lastly, results supported previous findings that evolving populations of small ssDNA viruses may maintain relatively high levels of genetic variation.