You clearly don’t. I do, though. All the stuff about ‘describing the relationship’ or whatever it is you’re saying - it’s completely irrelevant to the question. The terminology you want is ‘subject’, which is the part of the sentence that determines whether the declined verb should be singular or plural. This flower smells nice. These flowers smell nice. There’s no way that ‘with this promotion’, as a phrase, can ever be the subject of the sentence, and that it can control the verb - so it does not matter that promotion is singular. In this sentence, the phrase “new challenges and responsibilities” is the subject, and as it is plural, the verb needs to be plural as well. The resulting sentence may not be pretty, but there’s nothing ambiguous about it, and there’s no way in which using ‘comes’ is correct.