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, that is, 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 is developed to attach two different polymers (oligo(ethylene oxide) methacrylate and N,N-dimethylacrylamide) 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 initiators for continuous activator regeneration atom transfer radical polymerization and reversible addition-fragmentation chain transfer polymerization are not well-suited to bifunctional bioconjugates applications under the studied conditions. Nonetheless, the polymerization conditions preserve the native fold of the ubiquitin and enable production of a hetero-arm star protein-polymer bioconjugate.