Self-assembly of protein-polymer block copolymers is an attractive route for preparing biocatalytic materials. To clarify the effect of bioconjugate shape on self-assembly without changing the chemical details of either block, four different conjugation sites are selected on the surface of the model globular protein mCherry at residues 3, 108, 131, and 222 to alter the colloidal shape of the bioconjugate. All four mCherry-b-poly(N-isopropylacrylamide) bioconjugates show qualitatively similar phase diagrams, indicating that self-assembly is robust with respect to changes in conjugation site. However, protein orientation has an effect on the location of the order-disorder transition concentration, and the stability of the disordered micellar phase is shown to be different for each conjugate. Differences in domain spacing also suggest changes in protein orientation within the lamellae.