A numerical prediction is presented for upper bounds on negative floating potentials of shaded spacecraft surfaces, using a local-current-balance formulation. Results include the following: (1) By influencing the velocity-space cutoff boundaries for incident ion fluxes, the spacecraft geometry and sheath potential profile (particularly shaded-sunlit asymmetries in the latter) have large influences on shaded-surface potentials, which may exceed-20 kV in certain circumstances. (2) For electrically isolated surfaces in shaded cavities, negative floating potentials may exceed those on convex surfaces. (3) In some conditions, two distinct floating potentials are predicted. This implies the possibility of 'bifurcation phenomena' in which adjacent isolated surfaces made of the same material may follow different charging histories. It also implies that large and relatively sudden changes in surfaces potentials can be caused by gradual changes in either the external environment or beam emission currents.