Q: What are we supposed to be doing (right now)?
A: We are supposed to be studying (right now).
be supposed to functions as a quasi-modal and takes an infinitive as its object. Example:
We are supposed to go fishing today. ('fishing' is a gerund)
We are supposed to be at home studying. ('studying' is a gerund)
Note, separating the word studying from the word be is a good indication that be studying is not functioning as a progressive/continuous verb in our sentence.
studying is functioning as a gerund, which by the way, takes the form of a participle. That is, studying is both a participle (i.e. a present participle) and a gerund.
be supposed to + infinitive + nominal object (e.g. preposition, noun (gerund))
be supposed to functions as a quasi-modal and takes an infinitive as its object. <<
So, we can say "be doing" is the object of "are we supposed"?
And "doing" is a gerund?
Thank you for your reply.
With all respect to your answer, I still feel puzzled about this.
I somehow feel unsure, still, about "doing" functioning as a gerund, as "be" is part of the object as well. It seems that a present participle would follow "be" to me, and that the present participle would be part of the object. It seems strange that the infinitive "be" and a gerund would both be part of the same object. I think "doing" might be something else other than a gerund. I think it could be that it is actually a present participle within an object, or linked to the object "be".
In terms of what syntactic role 'studying' plays, structure tells me it's a noun but semantics tells me it's a progressive verb form. I remember reading somewhere some time ago that be + -ing functions as a pair, as a verb. Albeit, the fact that gerunds denote acts, yet function as non-acts, and, moreover, that "be" in our example sentence has a somewhat undefined ambiguity has me back at square one.
There's also the question of the subjunctive. Do such verbs take continuous verb forms as their objects? If not, gerund seems to be the better choice.
As for nominclature, 'to be studying' is the infinitive of "are studying", so there's no need to rename it.
I like your analysis. You've me 65% hooked. I await further evidence. :D