  We consider an extended version of the Kerr theorem incorporated in the
Kerr-Schild formalism. It allows one to construct the series of exact solutions
of the Einstein-Maxwell field equations from a holomorphic generating function
$F$ of twistor variables. The exact multiparticle Kerr-Schild solutions are
obtained from generating function of the form $F=\prod_i^k F_i, $ where $F_i$
are partial generating functions for the spinning particles $ i=1...k$.
Gravitational and electromagnetic interaction of the spinning particles occurs
via the light-like singular twistor lines. As a result, each spinning particle
turns out to be `dressed' by singular pp-strings connecting it to other
particles. Physical interpretation of this solution is discussed.
