There are some verbs or verbal periphrases which, even though they may not display the typical properties of ‘normal’, mainstream auxiliaries (the NICE properties), nonetheless share at least some of them. In particular, some verbal expressions which combine with contentful verbs can be shown to allow passivization in the same way as auxiliaries.
For this assignment, check this with the verb “have” in “have to” and with the verb “be” in “be to”. Both of which have modal, auxiliary-like meanings, and they might also behave like auxiliaries with respect to passivization.
First, compare the NICE properties of “be” in “be to” with those of progressive “be”, as well as those of have in have to as opposed to perfective have. Then check whether “be”, “have” in “be to”, “have to” behave like auxiliaries with respect to passivization.
When you are checking for passivization, make sure your infinitival verb is a transitive verb that can be passivized. If you use an intransitive verb no passive will be possible, but this will be because of reasons independing from the auxiliary nature of the first verb.
Thus, the fact that you cannot passivize with “John is sleeping a lot” (*A lot is being slept by John) is just a result of the fact that this is an intransitive verb and a lot is not the object, and it does NOT show that the progressive is not an auxiliary here.)
Write your assignment in a reasonably academic format. Make it short. You need not quote from any sources, but separate your examples from the text, number them and use italics.