Following the work of Koons (2001), we examine the statistical properties of extremely high fluxes of MeV electrons in the outer zone. We extend the analysis to include a variety of timescales and energies using observations from Los Alamos monitors at geosynchronous orbit and to include outer zone fluxes observed from L ~ 2--8 by spacecraft in highly elliptical Molniya orbits. We use the statistical formalism of the generalized extreme value distribution, which represents the probability distribution of the maximum value taken out of a sample of fixed size. By taking the maximum flux observed in many nonoverlapping intervals of several hours to several days, we can determine whether the maximum flux is likely to have a finite upper limit or an exponential or power law tail. Our analysis indicates that MeV electron fluxes over a broad range of energies, L shells, and timescales have a finite upper limit, a true worst case. However, the statistical estimate of this upper limit is inherently uncertain. We compare our upper limits to the internal charging specifications provided by Fennell et al. (2000). We discuss several possible physical explanations for the flux limits.