We investigate the electrical control of the spin–orbit (SO) interaction in GaAs wells, involving both one- and two-subband electron occupations altered by a gate potential Vg, over a wide range of well widths w's. Through the self-consistent Schrödinger–Poisson calculation, we determine all the intrasubband Rashba αν(ν=1,2) and Dresselhaus βν, and also the intersubband Rashba η and Dresselhaus Γ couplings. We observe two distinct regimes marked off around w=wc=30−35nm. In the first regime with w<wc, we find the usual behavior of SO couplings, i.e., the intrasubband Rashba couplings α1 and α2 have the same sign and both change almost linearly with Vg, while the Dresselhaus couplings β1 and β2 obeying the relation β1<β2 are almost constant. In contrast, in the second regime with w>wc, we observe that α1 and α2 can either have the same sign or opposite signs depending on Vg. In addition, even though α1 sensitively depends on Vg, we find that α2 remains essentially constant within a certain gate voltage range. As for the Dresselhaus couplings in this second regime, the inequality β1<β2 (valid in the first regime) only holds near the symmetric configuration of our wells, but otherwise the inequality tends to be reversed. On the other hand, we find that both the intersubband Rashba η and Dresselhaus Γ couplings change almost linearly with Vg in the first regime while in the second one a maximum of |η| occurs near the symmetric configuration. We also determined the persistent-spin-helix symmetry points of the two subbands, where the Rashba and the renormalized (due to cubic corrections) Dressehaus couplings are matched. We find that the helix symmetry for the second subband retains over a broad range of Vg's, thus possibly facilitating its locking in practice. Our results should be essential for experiments pursuing an universal electrical control of the SO interaction in semiconductor nanostructures.