Languages are known to vary in the number of verbs they exhibit corresponding to English be, in the distribution of such copular verbs, and in the presence or absence of a distinct verb for possession sentences corresponding to English have. This paper offers novel arguments for the position that such differences should be modeled in terms of suppletive allomorphy of the same syntactic element (here dubbed v BE ), employing a Late Insertion-based framework. It is shown that such a suppletive allomorphy approach to complex copula systems makes three predictions that distinguish it from non-suppletion-based alternatives (concerning decomposition, possible and impossible syncretisms, and Impoverishment), and that these predictions seem to be correct (although a full test of the possible and impossible syncretisms prediction is not possible in the current state of knowledge).