Consider a Calabi-Yau fourfold given as an elliptic fibration $\pi : X_4 \to B_3$ over a complex threefold. The discriminant locus $\{\Delta=0\}$ describes the locus in $B_3$ over which the elliptic curve degenerates. We can (usually, though perhaps not always) tune the fibration such that an $E_8$ singularity appears as a component of the discriminant locus. Generically this locus will have non-zero intersection with the rest of the discriminant locus, and at this locus (which is complex codimension two in $B_3$) the singularity will be worse than $E_8$.
I have heard on the one hand that such a singularity cannot be resolved with a crepant resolution (one which preserves the Calabi-Yau condition), and on the other hand that because of this we need to resolve these singularities. My question is then:
What is the appropriate way to resolve such a space to get a smooth Calabi-Yau fourfold? How does this differ from the case of resolving a less serious singularity?
In lieu of an answer, a useful reference would also be very appreciated.