The origins of novel traits are often studied using species trees and modeling phenotypes as different states of the same character, an approach that cannot always distinguish multiple origins from fewer origins followed by reversals. We address this issue by studying the origins of C-4 photosynthesis, an adaptation to warm and dry conditions, in the grass Alloteropsis. We dissect the C-4 trait into its components, and show two independent origins of the C-4 phenotype via different anatomical modifications, and the use of distinct sets of genes. Further, inference of enzyme adaptation suggests that one of the two groups encompasses two transitions to a full C-4 state from a common ancestor with an intermediate phenotype that had some C-4 anatomical and biochemical components. Molecular dating of C-4 genes confirms the introgression of two key C-4 components between species, while the inheritance of all others matches the species tree. The number of origins consequently varies among C-4 components, a scenario that could not have been inferred from analyses of the species tree alone. Our results highlight the power of studying individual components of complex traits to reconstruct trajectories toward novel adaptations.