May' in formulas for expressing wishes

May occurs in fixed phrases like:

May God be with you! May you live to be a hundred! May can also be used in the sense of 'We hope very much that...':

May there never be a nuclear war'

11 Modal auxiliaries and related verbs

11.72 'May/might'

11.72.1 'May/might (just) as well'

May as well and might as well can be used interchangeably to express the idea 'it makes no difference':

It's not very far, so we may/might as well go on foot May as well and might as well can differ as follows:

Shall we walk or take a bus?

- We may/might as well walk (i.e. it makes no difference) What a slow bus this is¹

- Yes, we might (Not *may*) just as well walk (i.e we'd get there more quickly)

11.72.2 'May/might/could well' = 'it is extremely likely'

May well might well and could well can be used interchangeably: He may/might/could well find that the course is too difficult

11.72.3 'May/might' in the sense of I grant you...'

This construction is often used in discussion and argument. Your typewriter may/might be a wonderful machine, but it's still old-fashioned compared with a word-processor

Might/could (at least)' in nagging complaints/reproach

You might (at least) clean the bathtub after you've used iV (I) might have + past participle of verbs like guess, know and suspect can reinforce complaint:

/ might have guessed he 'd fail to read the instructions

Might' in requests

Might can replace the imperative [> 9.52] in:

While you re out you might (no stress) post this letter for me

11.73 'Shall'

Apart from its main uses with I/we to refer to the future [> 9.36], and to make offers/suggestions [> 11.39-40], shall can be used with other persons (you, he, they, etc.) in e.g. the following ways [compare > 11.23]:

You shall pay for this (threat)