the sentence is "Will they decide if you should have been promoted?". The T' and AuxP are already taken up by 'have' and 'been, where does should go?
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2It depends on your theory of syntax, for instance in Adger’s Core Syntax it’s Mod. – Alex B. Nov 04 '20 at 23:42
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I changed the title (pending right now), so that this question won't get voted to be closed for asking for a syntax tree. – purlupar Nov 05 '20 at 05:03
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What theory of syntax are you using that says there can only be one AuxP? I'd expect there to be theories that either allow multiple AuxPs, or have specific categories for each auxiliary, a ModalP and PerfP for example. – curiousdannii Nov 05 '20 at 05:24
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1It's simply "should" (modal) + "have" (perfect aux) + "been" (either passive aux or progressive aux depending on the remainder of the clause. – BillJ Nov 06 '20 at 08:43