Mixed-initiative dialogs often contain interruptions in phrase structure such as repairs and backchannel responses. Phrase structure as traditionally defined does not accommodate such phenomena, so it is not surprising that phrase structure parsers are ill-equipped to handle them. This paper presents metarules that specify how phrase structure rules may be restarted or interrupted (including overlapping speech). In the case of overlapping speech or a backchannel response, the metarules allow a constituent to overlap or be embedded inside another constituent that it is unconnected to. In the case of repairs, the metarules operate on the reparandum (what is being repaired) and alteration (the correction) to build parallel phrase structure trees: one with the reparandum and one with the alteration. Consider the utterance, take the banum the oranges. The repair metarule would build two VPs, one being take the ban- and the other being take the oranges. The introduction of metarules simplifies the notion of an utterance since a sentence interrupted by an acknowledgment such as okay can still be one utterance formed around the interrupting acknowledgment. Together metarules and phrase structure rules specify the structures that should be accommodated by a parser for mixed initiative dialogs. A dialog parser should also maintain a dialog chart that stores the results of syntactic and semantic analysis of all of the dialog seen so far. This dialog chart will be a shared resource eliminating the need for maintenance of a separate representation of dialog structure by a dialog manager. In addition, the dialog parser can alert the dialog manager to utterances introducing obligations as well as recognizing acknowledgments and responses based on syntactic information.