  Cosmic rays have been shown to be extremely important in the dynamics of
diffuse gas in galaxies, helping to maintain hydrostatic equilibrium, and
serving as a regulating force in star formation. In this paper, we address the
influence of cosmic rays on galaxies by re-examining the theory of a cosmic ray
Eddington limit, first proposed by Socrates et al. (2008) and elaborated upon
by Crocker et al. (2021a) and Huang & Davis (2022). A cosmic ray Eddington
limit represents a maximum cosmic ray energy density above which the
interstellar gas cannot be in hydrostatic equilibrium, resulting in a wind. In
this paper, we continue to explore the idea of a cosmic ray Eddington limit by
introducing a general framework that accounts for the circumgalactic
environment and applying it to five galaxies that we believe to be a good
representative sample of the star forming galaxy population, using different
cosmic ray transport models to determine what gives each galaxy the best chance
to reach this limit. We show that while an Eddington limit for cosmic rays does
exist, for our five galaxies, the limit either falls at star formation rates
that are much larger or gas densities that are much lower than each galaxy's
measured values. This suggests that cosmic ray pressure is not the main factor
limiting the luminosity of starburst galaxies.
