We present the detection of CO(5-4) with S/N> 7 − 13 and a lower CO transition with S/N> 3 (CO(4-3) for 4 galaxies, and CO(3-2) for one) with ALMA in band 3 and 4 in five main sequence star-forming galaxies with stellar masses 3 − 6 × 10 10 M/M at 3 < z < 3.5. We find a good correlation between the total far-infrared luminosity L F IR and the luminosity of the CO(5-4) transition L CO(5−4) , where L CO(5−4) increases with SFR, indicating that CO(5-4) is a good tracer of the obscured SFR in these galaxies. The two galaxies that lie closer to the star-forming main sequence have CO SLED slopes that are comparable to other star-forming populations, such as local SMGs and BzK star-forming galaxies; the three objects with higher specific star formation rates (sSFR) have far steeper CO SLEDs, which possibly indicates a more concentrated episode of star formation. By exploiting the CO SLED slopes to extrapolate the luminosity of the CO(1-0) transition, and using a classical conversion factor for main sequence galaxies of α CO = 3.8 M (K km s −1 pc −2 ) −1 , we find that these galaxies are very gas rich, with molecular gas fractions between 60 and 80%, and quite long depletion times, between 0.2 and 1 Gyr. Finally, we obtain dynamical masses that are comparable with the sum of stellar and gas mass (at least for four out of five galaxies), allowing us to put a first constraint on the α CO parameter for main sequence galaxies at an unprecedented redshift.