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We present a CO(3−2) study of four systems composed of six (ultra) luminous infrared galaxies (U/LIRGs), located at 0.28 <z < 0.44, that straddle the transition region between regular star-forming galaxies and starbursts. These galaxies benefit from previous multiwavelength analysis allowing in depth exploration of an understudied population of U/LIRGs at a time when the universe is experiencing a rapid decline in star formation rate density. We detect CO(3−2) emission in four targets and these galaxies fall between the loci of regular star-forming galaxies and starbursts on the Kennicutt–Schmidtt relation. Compared to low luminosity LIRGs and high luminosity ULIRGs at similar redshifts, we find they all have similar molecular gas budgets with the difference in their star formation rates (SFR) driven by the star formation efficiency (SFE). This suggests that at these redshifts large molecular gas reservoirs must coincide with an increased SFE to transition a galaxy into the starburst regime. We studied the structure and kinematics and found our four detections are either interacting or have disturbed morphology which may be driving the SFE. One of the CO(3−2) non-detections has a strong continuum detection, and has been previously observed in H α, suggesting an unusual interstellar medium for a ULIRG. We conclude that our sample of transitioning U/LIRGs fill the gap between regular star-forming galaxies and starbursts, suggest a continuous change in SFE between these two populations and the increased SFE may be driven by morphology and differing stages of interaction.