Hybridization is increasingly recognized as a source of novel variation, but how hybridization can contribute to evolution is still not fully understood. Insights into the evolutionary potential of hybrid species, and the extent to which two parent species are constrained to form only a single specific hybrid phenotype, would increase our understanding of the impact of hybridization on evolution, adaptation and diversity. Here, I address these questions using the Italian sparrow (Passer italiae), a homoploid hybrid bird species formed from hybridization between house (P. domesticus) and Spanish sparrows (P. hispaniolensis). Using multivariate quantitative genetics methods, I examine four sexually dimorphic plumage traits (crown, back, rump and cheek) in males of all three species. For Italian sparrows, I compare three geographically separated island populations, which differ in genomic composition, to examine whether these populations vary in phenotype and whether they have more potential to evolve and diversify than the parent species. I show that the Italian sparrow is mosaic in its plumage pattern; some traits are similar to one of the parent species, others are similar to the other parent, but the Italian sparrow also has transgressive color values for back and rump (that is, outside the phenotypic range of either parent). In spite of strong parallelism in some traits, such as crown, island populations differ in some plumage traits, revealing that more than one phenotype can be formed by the same parent species. Alongside phenotypic novelty, the Italian sparrow has higher variability and evolvability than the parent species, showing that hybridization can indeed act as a source of new variation. However, my results indicate that, after initial hybridization, selection on secondary sexual signals can be strong along the axis of parental divergence in a hybrid species, as suggested by a pattern of low evolvability along this axis and fixation for one of the parental values for some traits in the Italian sparrow. This selection may be determined by inheritance patterns of parental female preferences in the hybrid species.