Will English speakers use 'be to be verb-ing' to form a sentence? See the examples below:
a) You are to be presenting your group project during the next lesson.
b) I am to be studying in school from 8am to 3:30pm.
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Marrying the two constructions BE to VERB and BE VERBing in the construction BE to be VERBing is syntactically acceptable.
However, it is very formal, and in many cases of little value.
BE to VERB itself is largely confined to very formal registers. Moreover, it is rather vague: I cannot think of a situation when it should be preferred to a more precise expression such as BE expected to VERB or BE required to VERB or BE scheduled to VERB or something else of that sort.
With 'atelic' verbs like study, run, sleep (verbs which don't have a 'built-in' endpoint or change of state), the progressive infinitive to BE VERBing adds nothing to the sense of the plain infinitive. It may be of some value in imposing an 'atelic' sense on a telic or ambivalent infinitive, such as to present, to make, to write.
It's good that you understand how this construction may be used; but I advise you to avoid it in your own work if it's not necessary. Your first example, for instance, appears to mean something which would be much more natural like this:
You are scheduled to present your group project during the next lesson.
Keep in mind, too, that the progressive itself may bear the sense of something expected or planned. If that's the sense you intend you may omit the BE to (or paraphrase) altogether:
You are presenting your group project during the next lesson.
Your second example is a little different. Here I suspect that what you mean is:
I am supposed to be in school studying from 8 to 3:30.
Studying there is not a progressive but an adjunctive participle. In some circumstances, however, a progressive may have emphatic or contrastive force:
I am supposed to be studying (not lollygagging) from 8 to 3:30.
I am supposed to be studying the whole time from 8 to 3:30.