We investigate the Rashba and Dresselhaus spin-orbit (SO) couplings in GaAs quantum wells in the range of well widths w allowing for a transition of the electron occupancy from one to two subbands. By performing a detailed Poisson-Schrödinger self-consistent calculation, we determine all the intra-and inter-subband Rashba (α 1 , α 2 , η) and Dresselhaus (β 1 , β 2 , Γ) coupling strengths. For relatively narrow wells with only one subband occupied, our results are consistent with the data of Koralek et al. [Nature 458 , 610 (2009)], i.e., the Rashba coupling α 1 is essentially independent of w in contrast to the decreasing linear Dresselhaus coefficient β 1 . When we widen the well so that the second subband can also be populated, we observe that α 2 decreases and α 1 increases, both almost linearly with w. Interestingly, we find that in the parameter range studied (i.e., very asymmetric wells) α 2 can attain zero and change its sign, while α 1 is always positive. In this double-occupancy regime of w's, β 1 is mostly constant and β 2 decreases with w (similarly to β 1 for the single-occupancy regime). On the other hand, the intersubband Rashba coupling strength η decreases with w while the intersubband Dresselhaus Γ remains almost constant. We also determine the persistent-spin-helix symmetry points, at which the Rashba and the renormalized (due to cubic corrections) linear Dresselhaus couplings in each subband are equal, as a function of the well width and doping asymmetry. Our results should stimulate experiments probing SO couplings in multi-subband wells.