The oxide interface SrTiO3/LaAlO3 supports a 2D electron liquid displaying superconductivity and magnetism, while allowing for a continuous control of the electron density using a gate. Our recent measurements have shown a similar surprising nonmonotonic behavior as function of the gate voltage (carrier density) of three quantities: the superconducting critical temperature and field, the inverse Hall coefficient, and the frequency of quantum oscillations. While the total density has to be monotonic as function of gate, the last result indicates that one of the involved bands has a nonmontonic occupancy as function of the chemical potential. We show how electronic interactions can lead to such an effect, by creating a competition between the involved bands and making their sturcture non-rigid, and thus account for all these effects. Adding Fock terms to our previous Hartree treatment makes this scenario even more generic.