Could have, might have, may have are fairly congruous if referring to the whether he stole the car (context 2)
I respectfully disagree, Hingehead. Each of those modal verbs covers a certain area of level of certainty.
'might' is the weakest epistemic modal. For pedagogical purposes in helping ESLs to get a grasp of modal epistemic meaning,
S [lexical verb] 100%
S almost certainly/must - 90-99%
S likely/probably/[should] - 51 to 89%
S may - 26 to 50% certainty
S might - 1 to 25% certainty
[S = subject]
'could' [and 'can'] just says "it is/was possible"
Context 1: he had the opportunity to steal the car but didn't take it
Context 2: that the car was stolen and he is possibly the person who stole it.
As far as having the opportunity to steal the car (context 1) 'could have' is the most common usage,
I'm not sure that 'could' is the most commonly used modal for this situation. I'd say that it depends on how much information the speaker has or how forceful the speaker wants to appear.
although some (particularly UK) can get a with 'he might have' but it's a little colloquial and tends to mean 'he should have'.
It only holds that meaning if that is the intended meaning. Otherwise, it can be pure modal speculation.
[/quote]'May have' would never be used in context 2.[/quote]
I don't understand this at all.
He may have stolen the car.