  The Khavinson-Shapiro conjecture states that ellipsoids are the only bounded
domains in euclidean space satisfying the following property (KS): the solution
of the Dirichlet problem for polynomial data is polynomial. In this paper we
show that a domain does not have property (KS) provided the boundary contains
at least three differrent irreducible algebraic hypersurfaces for which two of
them have a common point.
