We could reconstruct the evolution of eukaryote-specific molecular and cellular machinery if some living eukaryotes retained primitive cellular structures and we knew which eukaryotes these were. It's not clear that either is the case, but the expanding protist genomic database could help us in several ways.
Dacks, J. B., & Doolittle, W. F. (2001, November 16). Reconstructing/deconstructing the earliest eukaryotes: How comparative genomics can help. Cell. Cell Press. https://doi.org/10.1016/S0092-8674(01)00584-0