In the end, I think this question is related to this one (which was never satisfactorily answered), but I extend slightly and therefore am asking a new question.
In discussing the semiclassical model of electron dynamics (appropriate the slowly varying EM fields and subject to some more restrictions), Ashcroft and Mermin state that
The wave vector ofan electron is only defined to within an additive reciprocal lattice vector $\mathbf{K}$. One cannot have two distinct electrons with the same band index $n$ and position $\mathbf{r}$, whose wave vectors $\mathbf{k}$ and $\mathbf{k}'$ differ by a reciprocal lattice vector $\mathbf{K}$; the labels $n$, $\mathbf{r}$, $\mathbf{k}$ and $n$, $\mathbf{r}$, $\mathbf{k} + \mathbf{K}$ are completely equivalent ways of describing the same electron.
OK, I can accept that. But what about $n$, $\mathbf{r}$, $\mathbf{k}$ and $n$, $\mathbf{r}'$, $\mathbf{k}$, for $\mathbf{r} \neq \mathbf{r}'$: can two (different) electrons have these states? If so, how does this make sense? I know that the semiclassical model is a very odd "massaging" of the theory of $N$ electrons in equilibrium in a periodic potential towards describing transport for such a system, but in that equilibrium theory there is explicitly no mention of localization precisely because the Bloch eigenstates are delocalized. I am therefore very confused as to how we can have the quantum numbers $n$ and $\mathbf{k}$ applying to two different electrons (at different points in space) when these quantum numbers only make sense in describing electrons which are delocalizaed throughout a given macroscopic crystal in the first place!