-- Susan finds The Elegant Fisherman a completely overpriced restaurant. She never goes there. -- That's news to me. I saw her there with Tom last week. -- He might have offered to pay.
In the first example (mild annoyance), he might have offered = he should have offered.* In Clive's example, he might have offered = it is possible that he would have offered. In my example, he might have offered = it is possible that he did offer.
Oh, the joys of modal verbs!
CJ
*The first example is one of a general category of mo