Are they always interchangeable or subtle meaning differences occurred when we prefered one to another?
Here some sentences I came across. Can we rewrite these sentences with keeping their meanings?
General: We may have been able to save victims, we'll never know.(original sentence)
Possible variations:
General: We might have been able to save victims, we'll never know.
General: We could have been able to save victims, we'll never know.
General: We would have been able to save victims, we'll never know.
Another example sentence :
If he had worked harder, he may /might/could/would have been able to
get A at the exam.
Another example sentence :
I may/might/could/would have gone to university but I decided to get a
job.
Best Answer
Lost opportunities
The meanings of these are indistinguishable, except for a subtlety that I'll explain later:
The words "would" and "could" suggest both the past tense and the consequence of some imagined hypothesis, with either or both meanings being activated when suitable to the context. To use "would" here, you need to establish an imagined hypothesis. Then "would" indicates the consequence:
It's possible to say "could have been able to", but "could" is the past tense of "can", so it already indicates ability. So, "could have been able to save the victims" is awkward. However, you could say:
"Would have" and "could have" imply that the opportunity is now lost.
"May have", "might have", and "could have" don't require context to set up an imaginary hypothesis, but they do suggest that you have such a hypothesis in mind:
An important difference
A very big difference between the may/might and would/could sentences is that the would/could sentences claim a high level of certainty about the hypothetical situation: the antidote is assumed to work. The may/might sentences lack that certainty. They suggest only that in the hypothetical situation (which might not even be stated yet), the antidote might have worked. "Would" corresponds to "will", and says that the antidote will work (in the imagined situation, which occurred yesterday). "Could" corresponds to "can", and suggests that the antidote can work (in the imagined situation, which occurred yesterday).
A subtle difference
"May have" mainly indicates uncertainty about what we could have done. "Might have" suggests both uncertainty and that the opportunity, if it even existed, is now lost.
This is English, so don't take that as a rule. Instead, memorize this well-known couplet (by John Greenleaf Whittier, 1856):
One more power of might
There's one more possibility with "might", which illustrates the flexibility of these words. "Might" can suggest that the victims actually were saved, or are actually in the process of being saved:
In other words, the antidote we tried yesterday might be working, right now. Since the uncertainty of the word "might" applies to our ability to save the victims, if we had that ability yesterday, then our efforts yesterday were successful, or are on the way to succeeding. Currently, we don't know (that's the uncertainty of "might"). Obviously, your listener will hear this meaning only if the victims are still alive.
You can also do this with "may have" and "could have", but those don't make the pun in the title of this section. Since "may have" has the least connotation of lost opportunity, it provides the clearest way to express optimistic uncertainty about the effects of yesterday's action: "We may have saved the victims."