  We discuss and prove an extended version of the Kerr theorem which allows one
to construct 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$. Solutions have an unusual multi-sheeted
structure. Twistorial structures of the i-th and j-th particles do not feel
each other, forming a type of its internal space. Gravitational and
electromagnetic interaction of the particles occurs via the light-like singular
twistor lines. As a result, each particle turns out to be `dressed' by singular
pp-strings connecting it to other particles. We argue that this solution may
have a relation to quantum theory and to quantum gravity.
