  The X-ray spectra of the most extreme ultra-luminous X-ray sources -- those
with L > 1 E+40 erg/s -- remain something of a mystery. Spectral roll-over in
the 5-10 keV band was originally detected in in the deepest XMM-Newton
observations of the brightest sources; this is confirmed in subsequent NuSTAR
spectra. This emission can be modeled via Comptonization, but with low electron
temperatures (kT_e ~ 2 keV) and high optical depths (tau ~ 10) that pose
numerous difficulties. Moreover, evidence of cooler thermal emission that can
be fit with thin disk models persists, even in fits to joint XMM-Newton and
NuSTAR observations. Using NGC 1313 X-1 as a test case, we show that a patchy
disk with a multiple temperature profile may provide an excellent description
of such spectra. In principle, a number of patches within a cool disk might
emit over a range of temperatures, but the data only require a two-temperature
profile plus standard Comptonization, or three distinct blackbody components. A
mechanism such as the photon bubble instability may naturally give rise to a
patchy disk profile, and could give rise to super-Eddington luminosities. It is
possible, then, that a patchy disk (rather than a disk with a standard
single-temperature profile) might be a hallmark of accretion disks close to or
above the Eddington limit. We discuss further tests of this picture, and
potential implications for sources such as narrow-line Seyfert-1 galaxies
(NLSy1s) and other low-mass active galactic nuclei (AGN).
