In a narrative written in third person past tense, such as you'd find in most published books, can the phrase "may have" be used after verbs like "thought" or "said"? As a native English speaker,
- she never thought he may have done it
sounds wrong to me, but I'm struggling to explain why.
After some quick Google searches -- most of which led me back to this website -- I've ascertained that this has something to do with backshifting "may" into the past tense, but I can't figure out if "might have" is the only acceptable construction here, or if "may have" is grammatically correct as well.
I'm aware that many of these distinctions fall away in colloquial English, but I am concerned with how these verbs would be used in grammatically correct narrative writing.