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Contextuality is one particular phenomenon allowed by quantum theory that has no analogue in classical probability theory. A contextuality scenario (a.k.a. test space) refers to a specification of a collection of measurements which says how many possible outcomes each measurement has and which measurements have which outcomes in common. Given two independent systems, a natural question is how to represent such a situation as a single test space. In other words, how do two contextuality scenarios combine into a joint one? The answer to this was first proposed by Foulis and Randall , but does not encompass compositions among more than two systems. In the present work  we study how to extend their approach to describe scenarios with any number of independent components. We develop a family of extensions and show that, as long as classical, quantum or general probabilistic models are considered, all such extensions are "observationally equivalent". How other sets of probabilistic models behave under these different compositions is still an open question.  Foulis, D. J. and Randall, C. H. (1981) Empirical logic and tensor products, in H. Neumann (ed.),Interpretations and Foundations of Quantum Theory, Wissenschaftsverlag, Bibliographisches Institut 5, Mannheim/Wien/Z_rich, pp. 9?20.  Antonio Ac_n, Tobias Fritz, Anthony Leverrier, Ana Bel_n Sainz, Comm. Math. Phys. 334(2), 533-628 (2015).