Providing more than required amount of energy to an electron in an energy level
If the energy exceeds the minimum needed, there are a few possibilities:


More than one electron may be affected.
The electron(s) can be moved to yet higher levels within the atom.
The electron can be expelled (raised to a very high level) with the electron(s)' kinetic energy making up the difference.
At sufficiently high energy, pair production can occur.
Also, rather than expending all its energy on the electron, the photon can be scattered as a lower frequency (less energetic) particle (since it interacted at a point, I'd consider it a particle for that duration).


So -- the excess energy, in effect, can be shared between the photon and electron in varying proportions.

If less than the minimum amount to raise the electron's level is supplied, then the electron stays put... except for quantum phenomena such as tunneling. The Esaki diode exhibits negative resistance, where electrons are more likely to pass through the p/n junction with lower bias.