LaAlO 3 /SrTiO 3 and LaTiO 3 /SrTiO 3 heterostructures, exhibits a complex phase diagram controlled by the electron density. [1,2] While the system is in a weakly insulating state at low density, superconductivity emerges when electrons are added by means of electrostatic gating resorting to a back-gate, a side-gate, or a top-gate geometry [1,3,4] (Figure 1). When the carrier density (n 2D ) increases, the superconducting T c rises to a maximum value, c max T ≈ 300 mK, before decreasing as doping is further increased. The resulting dome-shaped superconducting phase diagram resembles that observed in other families of superconductors, including high-T c cuprates, Fe-based superconductors, heavy fermions, and organic superconductors. [5,6] Two noticeable doping points are universally observed in the phase diagram of oxide interfaces: a quantum critical point (QCP) at low density that separates a weakly insulating region and a superconducting one, and a maximum critical temperature point ( c max T ) at an optimal doping that defines the frontier between the underdoped regime and the overdoped one. Despite much research efforts, there is not yet a consensus on the origin of these two points. In LaAlO 3 /SrTiO 3 heterostructures, electrons A dome-shaped phase diagram of superconducting critical temperature upon doping is often considered as a hallmark of unconventional superconductors. This behavior, observed in SrTiO 3 -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 doublegate LaAlO 3 /SrTiO 3 field-effect device and Schrödinger-Poisson numerical simulations of the quantum well. The optimal doping point of maximum T c 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 T c 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 d xy 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 T c . 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.