Is it possible that there are extended simples—material objects extended in space or spacetime that have no proper parts? The most commonly cited argument for this possibility is based on a version of the Humean principle: namely (and with some qualifications), any pattern of instantiation of a fundamental relation is possible. In this paper, we make the Humean argument fully explicit, and criticise it from three aspects—the Disjunction problem, the Pluralist problem, and the Accidentality problem. First, the original argument only (...) shows a disjunctive thesis: either extended simples are possible, or unextended complexes are possible. In order to reach the desired conclusion, some additional premise is needed. Yet, even though we agree that the Disjunction problem can be met, we argue that the Humean argument fails to establish the possibility of extended simples, for two reasons: the first comes from compositional pluralism, and the second is about the definition of accidental properties. We contend that the latter two problems put the proponents of the Humean argument in serious difficulty. Thus, metaphysicians who hold that there are extended simples should find better arguments for this view. (shrink)