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This website shows "Modals of Possibility and Probability with Continuous Tenses"

Formula: SUBJECT + APPROPRIATE MODAL + BE + ING VERB

Person A: What’s all that noise?

Person B: The neighbour’s son is in a rock band. They must be practicing.

Formula: SUBJECT + APPROPRIATE MODAL + HAVE BEEN + ING VERB

Person A: I didn’t hear a sound when I passed by the children’s room earlier.

Person B: They must have been sleeping.

It also has a page showing Modals of Necessity, Prohibition, and Permission

I must renew my passport before I go on vacation.

I have to/ have got to renew my passport before I go on vacation.

Everyone should go to bed early tonight.

However, it doesn't have a page showing "Modals of Necessity, Prohibition, and Permission with Continuous tenses"?

My question is

Do we have Modals of Necessity, Prohibition, and Permission with Continuous tenses?

Can we say "He must be doing my homework at 3 o'clock" (strong obligation) or "Everyone should be sleeping at midnight" (advice)?

or when we say "He must be doing my homework at 3 o'clock" (we think it is a strong obligation), people will think that "must" is a Modal of Possibility. That is people may interpret that sentence as "There is very likely that he will be doing his homework at 3 o'clock"

and when we say "Everyone should be sleeping at midnight" (we think it is an advice), people will think that "should" here is a Modal verb of Possibility. That is people may interpret that sentence as "There is very likely that everyone will be sleeping at midnight"

I searched all over the internet but couldn't find any sites mentioning this.

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Yes. Those modals can be reinterpreted as you suggest. However, such a context would only be clear by using an emphatic intonation on the modal.

For example:

He MUST be doing my homework at 3 o'clock

would only make sense as a modal of possibility if you strongly emphasize the word must, and 2. the context makes such a statement clear. i.e. It's 3 o'clock now and you can't get in touch with your friend, so you suspect that the only way he wouldn't respond is if he's busy doing your homework.

Using such an emphatic statement outside of a warranted context will make the intended meaning unclear. Most people will then assume you mean it as a command or strong obligation.

The same holds for the other modals. They must have an emphatic intonation and the context must make the statement warranted. With should, for example:

Everyone SHOULD be sleeping at midnight

would be used if, let's say, it's around midnight and you hear snoring, but cannot see anyone sleeping, so you say the above sentence to imply what you believe to be the most likely case based on your available knowledge. The implication is that you would be surprised if the people were not sleeping at midnight.

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