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We are to meet at the post office.
You are to obey the law
Nothing was to be heard.
He is to become a scientist.
They were to meet again.
If you are to succeed, you must work hard.
He is to go abroad.

I am learning be to grammar and I was wondering if auxiliaries such as can, could, may, etc can be used for to be grammar, like

We can be to meet at the post office.
You may be to obey the law.
.
.

And I found this sentence The institute adds the move could be to strengthen internal unity.
I was wondering if could be to is also one of the be to grammars or this is just A=B like The plan is to learn English?

Thank you so much and happy new year!
Comments  
Hans51I am learning be to grammar and I was wondering if auxiliaries such as can, could, may, etc can be used for to be grammar, likeWe can be to meet at the post office.You may be to obey the law.
These aren't right. I can't think of any clearly correct examples of a modal being used with this sense of "be to". In fact, I can't actually think of a clear example of the infinitive "be" being used in this sense. Normally it is an inflection of "be", as in your first set of examples.
Hans51And I found this sentence The institute adds the move could be to strengthen internal unity.I was wondering if could be to is also one of the be to grammars or this is just A=B like The plan is to learn English?
In this case I most naturally understand "to" to mean "in order to", which is a different pattern from the above.
We are (scheduled, supposed, going) to meet at the post office. One of the intervening words has been omitted, and would be understood from the context. It is close in tone to the imperative form.

You are to obey the law. This is an alternate form of a command, perhaps more emphatic for "You must obey the law." or "Obey the law.)

The others follow a similar pattern.
Hans51I am learning be to grammar and I was wondering if auxiliaries such as can, could, may, etc can be used for to be grammar, likeWe can be to meet at the post office.You may be to obey the law.
No. Just as you cannot use these auxiliaries in the imperative. There is no sense of probability, possibility, ability in command-style language.
Hans51The institute adds the move could be to strengthen internal unity.
The sentence is not well-formed. This is perhaps what was meant:

The reason (that) the institute added the move could be to strengthen internal unity.

This is not a command or even close to the imperative tone. It has the sense of probability or possibility.
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I've found some sentences with "could be to (infinitive)" in the Internet [FrazeIt in English]:

"One solution could be to post larger signs, facing the trains, on the platforms.

Marine Lance Cpl. Chad Maynard was as proud as could be to serve in the Marines.

A solution could be to ignite a new, long lasting, and worthwhile national goal.

This could be to make inspection easier, to reduce splashing, or just tradition.

Imagine how inspiring it could be to see rugby that is as elegant as it is feral."

It my opinion, here, such a wording, i.e. be + to-infinitive, has nothing to do with giving orders or talking about arrangements. The following the verb "be" (a linking one) parts of the sentences like to post larger signs; to serve in the Marines; to ignite a new, long lasting, and worthwhile national goal; to make inspection easier, to reduce splashing, or just tradition; to see rugby are complements which refers back to the respective subjects in the sentences.
AlpheccaStarsThe sentence is not well-formed. This is perhaps what was meant:The reason (that) the institute added the move could be to strengthen internal unity.
In my opinion it is just about well-formed and means "The institute adds (i.e. further says/writes) that the purpose of the move (i.e. action, stance) could be to strengthen internal unity."

I do dislike this sort of omission of "that" though.
GPYI do dislike this sort of omission of "that" though.
Yes, it makes the text very difficult to decipher out of context.
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Hans51I am learning be to grammar
There is no "be to"! The idiom you are working with is usually called "is to". It only exists in five forms.

am to, is to, are to, was to, were to.

Note that there is no "be to". The infinitive form does not exist for the idiom in question. Any other combination you see is unrelated to this particular idiom. 'We can be to' and 'You may be to' are thus impossible.
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In the other examples you cite there is simply a coincidence of a modal verb, a linking verb, and an infinitive complement.

The institute adds (that) | the move | could be | to strengthen internal unity.

is a modal variant of

The institute adds (that) | the move | is | to strengthen internal unity.

Briefly,

The (reason for the) move | is | to strengthen unity. where 'is' acts as an equal sign.

CJ