  We describe quantum phase transitions in superconducting complex oxides which
could be tuned by electrostatic charge transfer. Using a simple model for the
superconductivity of a thin film or surface of a bulk copper oxide, we show
that tuning the carrier density may allow the visitation of several
superconducting phases with different pairing symmetries such as extended $s$-
$(se)$, $d$- and $(se \pm id)$-wave. We construct a universal phase diagram for
single-band superconductors with $se$- and d-wave components of the order
parameter based on symmetry considerations alone. For a specific model with
nearest neighbor attraction, we obtain the phase diagram in the interaction
versus filling factor space showing the boundaries of the possible phases.
Finally, we calculate the superfluid density and penetration depth as
characteristic properties of each phase.
