This paper explores possibilities of implementing the Strong Minimalist Thesis (SMT) of Chomsky (2000, 2001, 2004) in the particular empirical domain of the computational system of human language (see (1)). Capitalizing on some specific approach to multiple spell-out and its interesting application to some concrete linguistic phenomena (Epstein et al., 1998; Lopez, 2003), it shows that the \u27invasion\u27 property of a number of external modules inter facing narrow syntax in the sense of Epstein et al. (1998; see also Lopez, 2003, and its modification in the present paper) may have certain restricting effects on one of the central assumptions of the cartography project (Rizzi, 1997; Cinque, 1999, Cinque (Ed.), 2002; Rizzi (Ed.), 2004; Bell...