My book says that
Since the number of electrons lost must equal the number gained, the half-reactions must be multiplied by integers as necessary to achieve the balanced equation. However, the value of e° is not changed when a half-reaction is multiplied by an integer. Since a standard reduction potential is an intensive property (it does not depend on how many times the reaction occurs), the potential is not multiplied by the integer required to balance the cell reaction.
However, I do not understand why the reduction potential is unaffected by the number of mols. If you have a greater number of mols of the metal, doesn't that allow for a greater potential difference?