  We present a catalog of all CO (J=4-3 through J=13-12)), [CI], [NII] lines
available from extragalactic spectra from the Herschel SPIRE Fourier Transform
Spectrometer (FTS) archive combined with observations of the low-J CO lines
from the literature and from the Arizona Radio Observatory. This work examines
the relationships between LFIR, L'CO, and LCO/LCO(1-0). We also present a new
method for estimating probability distribution functions (PDFs) from marginal
signal-to-noise ratio Herschel} FTS spectra, which takes into account the
instrumental "ringing" and the resulting highly correlated nature of the
spectra. The slopes of log(LFIR) vs. log(L'CO) are linear for all mid- to
high-J CO lines and slightly sublinear if restricted to (U)LIRGs. The mid- to
high-J CO luminosity relative to CO J=1-0 increases with increasing LFIR,
indicating higher excitement of the molecular gas, though these ratios do not
exceed ~ 180. For a given bin in LFIR, the luminosities relative to CO J=1-0
remain relatively flat from J=6-5 through J=13-12, across three orders of
magnitude of LFIR. A single component theoretical photon-dominated region (PDR)
model cannot match these flat SLED shapes, though combinations of PDR models
with mechanical heating added qualitatively match the shapes, indicating the
need for further comprehensive modeling of the excitation processes of warm
molecular gas in nearby galaxies.
