Modals/Reported Speech

Question

İn reported speech for example we change may to might and might or should stay the same like :

 She said "I should do my homework this night.".
 She said that she should do her homework last night.

 He said "I  may go abroad this year."
 He said that he might go abroad last year.

But i learned that the past forms of modal verbs are "may have past participle", "might have pp", "should have pp". Why do we use " may do", "might do", "should do" to refer to the past for prevent confusions in meaning, or are there different reasons ?

["One problem with English modals is that they have very few forms and constructions to express very many possible situations, so each form or construction has to cover many possibilities. Your examples take us into territory where there are more distinctions to be drawn than the language has tools for; consequently, much of what is meant must be inferred from context rather than from the actual words."] "Should do" or " might do" don't refer to past, but we use them in reported speech as past form, because modal verbs don't have much forms but they have to express many situation. İf we use "should have" or "might have" in every reported speech to refer to someones speechs occured in the past,they can express different meanings which we don't want to imply.Am i right ? İ want your help i cannot understand this issue help me and give me some examples to clarify.

Answer 1

Historically, many of the modals are in pairs, present and past: will and would; can and could; shall and should; may and might.

But in modern English, these relationships are much weaker, and some have disappered for most people, as the formally past forms have acquired their own separate meanings. (Particularly might as the past of may).

So in reported speech, most speakers will still change will to would, and can to could; and those who use shall will change it to should. Eg Can you do it? vs _He asked if I could do it. But not everybody changes may to might, I think.

But the "past" forms would, could, should, might, also have their own separate meanings, and these do not change in reported speech; eg Could you help me? vs I asked if he could help me.

The forms with have (eg could have) are not used as past forms for reported speech, but are used for counter-factuals (I believe ESL teachers call this the "third conditional"). Eg I could have done it if I'd had time vs He could have done it if he'd had time.