We report on detections of the high-excitation CO J=6–5 , J=4–3 lines in Mrk 231 , a prototypical Ultra Luminous Infrared Galaxy ( ULIRG ) and Seyfert 1 QSO . These observations are combined with CO J=3–2 , HCN J=4–3 ( this work ) , and CO J=2–1 , J=1–0 , ^ { 13 } CO J=2–1 , HCN J=1–0 measurements taken from the literature to provide better constraints on the properties of the molecular gas in an extreme starburst/QSO in the local Universe . We find that the CO J=4–3 and J=6–5 transitions trace a different gas phase from that dominating the lower three CO transitions , with n ( H _ { 2 } ) \sim ( 1 - 3 ) \times 10 ^ { 4 } cm ^ { -3 } and T _ { k } \sim ( 40 - 70 ) K . This phase is responsible for the luminous HCN emission , and contains most of the H _ { 2 } gas mass of this galaxy . The total CO line cooling emanating from this dense phase is found similar to that of the [ C ii ] line at 158 \mu m , suggesting a very different thermal balance to that seen in lower IR-luminosity galaxies , and one likely dominated by dense photon-dominated regions . Our dense “ sampling ” of the CO rotational ladder and the HCN lines enables us to produce well-constrained Spectral Line Energy Distributions ( SLEDs ) for the dense molecular gas in Mrk 231 and compare them to those of high redshift starbursts , many of which have SLEDs that may be affected by strong lensing . Finally , we use our local molecular line excitation template to assess the capabilities of future cm and mm/sub-mm arrays in detecting CO and HCN transitions in similar systems throughout the local and distant Universe .