Is the Fermi Surface Relevant for Metals with Band Structure?

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Does this construction even make sense? By definition it is a surface of constant energy in k-space, so for the free electron it is a sphere. But for metals you have band structure so that a given k-vector can have several different energies associated with it.
Which of these are to be chosen?

 

[mfb]

For free electrons (or for an approximation), choose the model for free electrons, otherwise don't choose that?
Electrons in metals see a potential structure, if this can be neglected or not depends on your problem.