Octahedral faceted nanoparticles are highly attractive fuel cell catalysts as a result of their activity for the oxygen reduction reaction (ORR). However, their surface compositional and morphological stability currently limits their long-term performance in real membrane electrode assemblies. Here, we perform in situ heating of compositionally segregated PtNi_1.5 octahedral nanoparticles inside a transmission electron microscope, in order to study their compositional and morphological changes. The starting PtNi_1.5 octahedra have Pt-rich edges and concave Ni-rich {111} facets. We reveal a morphological evolution sequence, which involves transformation from concave octahedra to particles with atomically flat {100} and {111} facets, ideally representing truncated octahedra or cuboctahedra. The flat {100} and {111} facets are thought to comprise a thin Pt layer with a Ni-rich subsurface, which may boost catalytic activity. However, the transformation to truncated octahedra/cuboctahedra also decreases the area of the highly active {111} facets. The morphological and surface compositional evolution, therefore, results in a compromise between catalytic activity and morphological stability. Our findings are important for the design of more stable faceted PtNi nanoparticles with high activities for the ORR.