  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 multi-wavelength 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$\alpha$, 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.
