  Solutions for the static spherically symmetric extremally charged dust in the
Majumdar--Papapetrou system have been found. For a certain amount of the
allocated mass/charge, the solutions have singularities of a type which could
render them physically unacceptable, since the corresponding physically
relevant quantities are singular as well. These solutions, with a number of
zero-nodes in the metric tensor, are regularized through the $\delta$-shell
formalism, thus redefining the mass/charge distributions. The bifurcating
behaviour of regular solutions found before is no longer present in these
singular solutions, but quantized-like behaviour in the total mass is observed.
Spectrum of regularized solutions restores the equality of the
Tolman--Whittaker and ADM mass, as well the equality of the net charge and ADM
mass, which is the distinctive feature of Majumdar--Papapetrou systems.
