Luminous infrared galaxies (L-IR > 10(11) L-circle dot) are often associated with interacting galactic systems and are thought to be powered by merger-induced starbursts and/or dust-enshrouded active galactic nucleus. in such systems, the evolution of the dense, star-forming molecular gas as a function of merger separation is of particular interest. Here, we present observations of the CO(3-2) emission from a sample of luminous infrared galaxy mergers that span a range of galaxy-galaxy separations. The excitation of the molecular gas is studied by examining the CO(3-2)/CO( 1 -0) line ratio, r(31), as a function of merger extent. We find these line ratios, r(31), to be consistent with kinetic temperatures of T-k = (30-50) K and gas densities of n(H2) = 10(3) cm(-3). We also find weak correlations between r(31) and both merger progression and star formation efficiency [L-FIR/LCO(1-0)]. These correlations show a tendency for gas excitation to increase as the merger progresses and the star formation efficiency rises. To conclude, we calculate the contributions of the CO(3-2) line to the 850-mu m fluxes measured with SCUBA (Submillimetre Common-User Bolometer Array), which are seen to be significant (similar to 22 per cent).