International audienceWe address the syntax and parametric variation underlying the verb 'have' from the empirical domain of Breton diachronic and dialectal variation. We introduce the Celtic agreement system characterized by Complementarity Effects and show why Breton 'have' is special among the Celtic language and at the same time unique among Breton verbs. We propose syntactic tests for decomposing the structure of 'have'. With these tools in hand, we show that 'have' across Breton dialects appears to trace an ordered path in UG parameter space from a strictly analytic mihi est to a fully lexicalized 'have'. We develop the predictions our proposal makes internally to each dialect, and list predictions to be checked in future data collect...