The wikipedia every on photoelectric effect has the following line
Electrons can absorb energy from photons when irradiated, but they usually follow an "all or nothing" principle. All of the energy from one photon must be absorbed and used to liberate one electron from atomic binding, or else the energy is re-emitted. If the photon energy is absorbed, some of the energy liberates the electron from the atom, and the rest contributes to the electron's kinetic energy as a free particle.
Now the wikipedia entry uses the word usually rather than always so are there any cases where this all or nothing principle is not followed.
PS: exclude the case in which an orbit transfer may occur.