  We prove that for every $n\geq 2$ the class of all finite $n$-partite
tournaments (orientations of complete $n$-partite graphs) has the extension
property for partial automorphisms, that is, for every finite $n$-partite
tournament $G$ there is a finite $n$-partite tournament $H$ such that every
isomorphism of induced subgraphs of $G$ extends to an automorphism of $H$. Our
constructions are purely combinatorial (whereas many earlier EPPA results use
deep results from group theory) and extend to other classes such as the class
of all finite semi-generic tournaments.
