The Agree operation as formalized by Chomsky (2000) is undefined for ambiguous domains. A probing domain is ambiguous when there are multiple visible matches in it, but none of them asymmetrically c-commands all the others. In such domains, no unique match can be distinguished as being the one hierarchically closest to the probe, and therefore the Agree operation cannot be triggered. For instance, if the domain of a φ-agreeing complementizer includes a visible coordinate clause (IP coordination), it is ambiguous. In this paper I look at sentences that instantiate such configurations and note that a dependency is established with the match linearly closest to the probe. Since the precise dependency under discussion, switch-reference, determines morphological as well as semantic effects, it must be determined before spell-out by Agree. This has drastic consequences for the architecture of the grammar. It requires that word order be determined early enough, in the narrow syntax, and motivates an addendum to Agree that specifies that, inside ambiguous domains, Agree is triggered by the match linearly closest to the probe.