  The luminosity range at and just below the 10^39 erg/s cut-off for defining
ultraluminous X-ray sources (ULXs) is a little-explored regime. It
none-the-less hosts a large number of X-ray sources, and has great potential
for improving our understanding of sources with ~Eddington accretion rates. We
select a sample of four sources in this Eddington Threshold regime with good
data for further study; these objects possess a variety of soft spectral
shapes. We perform X-ray spectral and timing analysis on the XMM-Newton and
Chandra data for these objects to gain insight into their accretion mechanisms,
and also examine their optical counterparts using HST images. NGC 300 X-1 is a
highly luminous and well-known example of the canonical steep power-law
accretion state. M51 ULS exhibits a cool blackbody-like spectrum and is
consistent with being an ultraluminous supersoft source (ULS), possibly a
super-Eddington accreting object viewed at a high inclination through an
optically thick outflowing wind. NGC 4395 ULX-1 and NGC 6946 ULX-1 have
unusually steep power-law tails, for which we discuss a variety of possible
physical mechanisms and links to similar features in Galactic microquasars, and
we conclude that these sources are likely intermediate objects between the soft
ultraluminous regime of ULXs and classic ULSs.
