  We report on new sensitive CO J=6-5 line observations of several luminous
infrared Galaxies (LIRGs: L$_{\rm IR}$(8-1000$\mu $m$)\ga 10^{11}$
L$_{\odot}$), 36% (8/22) of them ULIRGs (L$_{\rm IR}$$>10^{12}$ L$_{\odot}$),
and two powerful local AGN: the optically luminous QSO PG 1119+120, and the
powerful radio galaxy 3C 293 using the James Clerk Maxwell Telescope (JCMT) on
Mauna Kea in Hawaii. We combine these observations with existing low-J CO data
and dust emission Spectral Energy Distributions (SEDs) in the far-infrared -
submillimetre from the literature to constrain the properties of the
star-forming ISM in these systems. We then build the first {\it local} CO
Spectral Line Energy Distributions (SLEDs) for the {\it global} molecular gas
reservoirs that reach up to high J-levels. These CO SLEDs are neither biased by
strong lensing (which affects many of those constructed for high-redshift
galaxies), nor suffer from undersampling of CO-bright regions (as most current
high-J CO observations of nearby extended systems do). We find: ...
