A dome-shaped phase diagram of superconducting critical temperature upon doping is often considered as a hallmark of unconventional superconductors. This behavior, observed in SrTiO3-based interfaces, whose electronic density is controlled by field-effect, has not been explained unambiguously yet. Here, a generic scenario for the superconducting phase diagram of these oxide interfaces is elaborated based on transport experiments on a double-gate LaAlO3/SrTiO3 field-effect device and Schrödinger–Poisson numerical simulations of the quantum well. The optimal doping point of maximum Tc is ascribed to the transition between a single-gap and a fragile two-gap s±-wave superconducting state involving bands of different orbital character. Close to this point, a bifurcation in the dependence of Tc on the carrier density, which can be controlled by the details of the doping execution, is observed experimentally and reproduced by numerical simulations. Where doping with a back-gate triggers the filling of a new subband and initiates the overdoped regime, doping with a top-gate delays the filling of the subband and maintains the 2D electron gaz in the single-gap state of higher Tc. Such a bifurcation, whose branches can be followed reversibly, provides a generic explanation for the dome-shaped superconducting phase diagram that could be extended to other multiband superconducting materials.