  We construct families of fermionic projectors with spherically symmetric
regularization, which satisfy the condition of a distributional ${\mathcal{M}}
P$-product. The method is to analyze regularization tails with a power-law or
logarithmic scaling in composite expressions in the fermionic projector. The
resulting regularizations break the Lorentz symmetry and give rise to a
multi-layer structure of the fermionic projector near the light cone. The
remaining freedom for the regularization parameters and the consequences for
the normalization of the fermionic states are discussed.
