1. He may have stolen the money.

2. He might have stolen the money.
3. He can have stolen the money.
4. He could have stolen the money.
------------------------------------
Is #3 ungrammatical? Are #2 and #4 the same in meaning? They both have slight or uncertain possibility. Is that right? #2 has slighter probability than #1, doesn't it?

#3 would not be used.

The other three sentences mean approximately the same thing.

Regarding the grammaticality of sentence #3, "He can have stolen the money," it is grammatically correct. However, it is not commonly used to express a hypothetical past action or uncertainty, unlike sentences #1, #2, and #4.

In terms of meaning, sentences #2 ("He might have stolen the money") and #4 ("He could have stolen the money") are very similar and often used interchangeably. Both sentences indicate a lesser degree of possibility or uncertain speculation about a past event. The difference between them lies in the level of probability inferred.

Sentence #2 suggests a slightly lesser probability compared to sentence #1 ("He may have stolen the money"). So, you are correct in observing that #2 has a slighter probability than #1. The word "might" implies a smaller likelihood or a more hypothetical scenario.

Sentence #4 ("He could have stolen the money") suggests a bit stronger possibility compared to #2. The word "could" suggests that the action of stealing the money is more plausible but still uncertain.

To summarize, #2 and #4 share a similar meaning with slight or uncertain possibility, but the use of "might" in #2 indicates a slightly lower probability than "could" in #4.