Protein-polymer bioconjugates present a way to make enzymes more efficient and robust for industrial and medicinal applications. While much work has focused on mono-functional conjugates, i.e. conjugates with one type of polymer attached such as poly(ethylene glycol) or poly(N-isopropylacrylamide), there is a practical interest in gaining additional functionality by synthesizing well-defined bifunctional conjugates in a hetero-arm star copolymer architecture with protein as the core. Using ubiquitin as a model protein, a synthetic scheme was developed to attach two different polymers (OEOMA and DMAm) directly to the protein surface, using orthogonal conjugation chemistries and grafting-from by photochemical living radical polymerization techniques. The additional complexity arising from attempts to selectively modify multiple sites led to decreased polymerization performance and indicates that ICAR-ATRP and RAFT are not well-suited to bifunctional bioconjugates applications. Nonetheless, the polymerization conditions preserve the native fold of the ubiquitin and enable production of a hetero-arm star protein-polymer bioconjugate.