They are a "special" class of beings in regard to distinguishing the generated from what is not generated.

In Aristotle all beings are generated.

Except for the forms and matter which make such beings possible.

Except for the forms and matter which make such beings possible. — Paine

But form and matter are not separate beings. Form and matter are principles of Aristotle's physics, which are applied toward understanding being, such that we can say that a being necessarily consists of both. Primary substance is individuals, and individuals consist of both form and matter.

They are not separated in the generated individual, but Aristotle distinguishes between the soul as form and the individual repeatedly as the bulk of my quotes demonstrate. De Anima begins with the distinction:

There is also the problem of whether the affections (πάθη) of the soul are all common also to that which has it or whether any are peculiar to the soul itself; — ibid, 403a3-7, Greek terms included by Eugene T. Gendlin

After Aristotle develops his proposed answer to the problem he can say:

Hence old age is not due to the soul's being affected in a certain way, but this happening to that which the soul is in, as in the case of drunkenness and disease. — ibid, 408b 18, emphasis mine

The book is meaningless without the distinction.

They are not separated in the generated individual, but Aristotle distinguishes between the soul as form and the individual repeatedly as the bulk of my quotes demonstrate. De Anima begins with the distinction: — Paine

The soul, as the form of the individual, is not a being which is separate from the matter, nor is it an intellect. The soul is a type of actuality which is necessarily prior to the material body, as the cause of it. A cause must be an actuality. That's what I tried to explain to you before, but you seem to want to describe the soul as some sort of intellect which persists after the material body. The intellect, as a power of the soul is a potency, or potential, though. And we have no principles to support the idea of a cause persisting after its effects.

The intellect is a property of what you call a combined (material) being. There is no principle to support an "active intellect" which "exists separately". The idea of a "separate form" is supported by the necessity of a cause (the soul in this case) preceding its effect (material body). The soul must be separate because it necessarily exists when there is no material body, prior to it, because of the temporal nature of "cause"; it is prior to the material body. As necessarily actual, Aristotle assigns "the soul" to the category of "form" But the intellect, as a potential (from the passage I quoted), is posterior to the material body, dependent on it, just like every other power that the soul has. Each and every one of the soul's potencies is dependent on, therefore not separable, from the body. In the case of the intellect, this is demonstrated by the example, the intellect is dependent on the imagination. The idea of a separate active intellect is a notion which is left unjustified.

Apart from the question of whether causes and first principles exist outside of the individual beings they bring into existence, they can be distinguished from each other during the inquiry into their nature. What, after all, is an inquiry into causes if one cannot make that distinction?

The soul is the cause and first principle of the living body. But these are so spoken in many ways, and similarly the soul is cause in the three ways distinguished; for the soul is cause as being that from which the movement is itself derived, as that for the sake of which it occurs, and as the essence of bodies which are ensouled. — De Anima, 415b8, translated by D.W. Hamlyn

But the intellect, as a potential (from the passage I quoted), is posterior to the material body, dependent on it, just like every other power that the soul has. — Metaphysician Undercover

The potentiality of the intellect in III.4 is not described as a dependency upon the "material body" but as a condition that allows it to think "all things":

It must, then, since it thinks all things, be unmixed, as Anaxagoras says, in order it may rule, that is in order it may know; for the intrusion of anything foreign to it hinders and obstructs it; hence too, it must have no other nature than this, that is potential. That part of the soul, then, called intellect (and I speak of as intellect that by which the soul thinks and supposes) is actually none of the existing things before it thinks. Hence too, it is reasonable that it should not be mixed with the body; for in that case it would come to be of a certain kind, either cold or hot, or it would even have an organ like the faculty of perception; but as things are it has none. Those who say, then, that soul is a place of forms speak well, except it is not the whole soul but that which can think, and it is not actually but potentially the forms. — ibid, 429a 18

This is the last comment I will make in this discussion. Feel free to have the last word. I am still no closer to understanding your interpretation and you report the same consternation about mine. It is time that I exit the revolving door.

part from the question of whether causes and first principles exist outside of the individual beings they bring into existence, they can be distinguished from each other during the inquiry into their nature. What, after all, is an inquiry into causes if one cannot make that distinction?

The soul is the cause and first principle of the living body. But these are so spoken in many ways, and similarly the soul is cause in the three ways distinguished; for the soul is cause as being that from which the movement is itself derived, as that for the sake of which it occurs, and as the essence of bodies which are ensouled.
— De Anima, 415b8, translated by D.W. Hamlyn

But the intellect, as a potential (from the passage I quoted), is posterior to the material body, dependent on it, just like every other power that the soul has.
— Metaphysician Undercover

The potentiality of the intellect in III.4 is not described as a dependency upon the "material body" but as a condition that allows it to think "all things": — Paine

Do you apprehend a difference between the soul, as "the cause and first principle of the living body", and the intellect, as "a condition which allows it to think 'all things'"? The latter is posterior to the former, as the former is the cause of being of the latter.

Also, the potentiality of the intellect is definitely described as dependent on the material body. That's the point of the reference to imagination. Thinking requires imagination, which requires the bodily senses. That's how Aristotle describes all the powers of the soul, the higher are dependent on the lower, and they are all features of the various living bodies. We can conclude that the powers, or potencies, of the soul are materially based, because in his physics, matter provides the potential for change. They are potential, therefore they are materially based.

He demonstrates that the powers exist as potential, by explaining that any of the powers is not active all the time, it must be actualized. So the power resides in the potential (we can conclude matter). Aquinas looked at this with respect to the nature of "habit", and found that the habit, even though it is a specific way of acting, resides in the potential, material aspect, not in the act itself, the formal aspect.

I am still no closer to understanding your interpretation and you report the same consternation about mine. — Paine

I have to admit, I do not see the point you are trying to argue. There appears to be no consistency to what you say. You assert an "active intellect" which "exists separately", but then you readily admit to the obvious, that Aristotle describes the intellect as a potential, in all of its facets. When attempting to support the idea of a separate "active intellect", you refer back to "the soul", as if there's no separation between the soul and the intellect. But you need to respect the fact that the intellect is a product of the soul, just like all the other powers of the soul, which are all features of the material body. In describing the intellect, you cannot refer directly to the soul, because one is just a property of the other.