And it should be noted that, as the Philosopher says in Metaphysics V, possible and impossible are said in one way absolutely, namely, because in themselves they can be true or cannot be true by reason of the relationship existing between the terms; in another way a thing is said to be possible or impossible to something, namely, what it is able for with respect to its active or passive power. And it is in this sense that "possible" and "impossible" are taken here, namely, as what is, or is not, within the power of an agent or patient - for this is the meaning that is most appropriate to natural things.
Likewise I think we would see that, whatever problems there may be with the argument, one of the counterexamples very commonly put forward against it is not a counterexample at all. I quote Wippel's summary of it:
Why not rather suggest that one possible being has come into being after another, and that after another, extending backwards into a beginningless past? Under this supposition, some possible being or beings will have existed at any given point in time, although no single possible being will have existed from eternity.
[John Wippel, "The Five Ways," Thomas Aquinas, Brian Davies, ed. Oxford UP [Oxford: 2002] p. 176.]
This is supposed to be a counterexample to the claim that "It is impossible for all things that are, to be such [i.e., possibly not being in the sense relevant to generation and corruption], because what possibly is not being, is at some time or other not." But this is singularly what it fails to be. The underlying idea involved in Aquinas's discussions of possibility and necessity in generation is the actual ability to exist for a duration, given the nature of things. Something that possibly exists and possibly doesn't exist means that it has the actual ability, given its generating causes and its nature, of existing for a specific period of time and the actual ability, given its nature and generating causes, of not existing outside that specific period of time; and this is an ability that must be exercised, because if you say that something began to exist at a specific point in time because of its generating causes and its generable nature, you are saying that it had the ability to begin to exist from that point on, and not prior. And likewise, if you destroy something, it no longer has the actual ability to exist, but only the actual ability not to exist. If it has the ability to exist for a specific period of time, it exists; and if it doesn't, it doesn't. Thus in this very technical sense of the term it's a contradiction to say that something possibly is and possibly is not at the same time: this would be to say that its causes and nature are set up so that it both exists and does not exist in that period of time, which is a contradiction. Now something counts as necessary in the same way if its causes and nature are such that it exists at every time. Some of these things exist always because of their nature, some because they are made to exist. But if it exists always, it is necessary and not possible, since in the sense being used here necessity is an actual ability to exist at every time and possibility is a actual ability to exist some, and only some, times. And since 'generable' and 'destructible' are coextensive, an existing thing that by the nature of things is ingenerable is indestructible; so, if one accepts the arguments in the De Caelo commentary (which are really the trickiest and hardest part of the whole account), if something by nature has never been generated it will by nature never be destroyed, and this is to be necessary in the sense relevant to generation.
But given this we see why the supposed counterexample is not a counterexample: the world insofar as it consists of the series will have always existed, and therefore will be ingenerable, and therefore will be classified as necessary, and therefore not as possible. Therefore the scenario doesn't present a case in which everything would be possible, and is not a counterexample to the claim that not everything can be possible (in the relevant sense). Faced with such a series, we would have to ask, in Aristotelian terms, whether the series itself had some feature that made it necessary to exist or if it were made necessary to exist by some cause (which itself would have to be necessary to exist in order to have that sort of effect); that is, the argument would proceed exactly as it would if there were no such series.
And this, if you think about it, makes entire sense: while Aquinas holds that the world was created, he accepts the Aristotelian claim that it is ingenerable and indestructible, and he can do this because creation and generation are two entirely different things: Aristotle has no concept of creation in the Christian sense, and trying to treat creation and generation as the same thing will get you immediately into contradictions. This is why Aquinas holds that it is possible for the world always to have existed: there is no impediment to it either from the nature of the world (which is such that if it exists it can neither be generated nor destroyed in the Aristotelian sense) nor from its cause (which is God omnipotent, cause of existence for everything that can be made to exist). The argument is built out of Aristotle's account of generation, but the supposed counterexample depicts a situation that is on Aristotle's own account the way the world actually is, and on Aquinas's account a way in which God could have created it. If the world were possible in the sense relevant to the Aristotelian account of generation, it could not exist without being generated at some point in time after it had not existed. So it is necessary, being such that it cannot be generated or destroyed; but it can still be created. Explaining this, in fact, is how Aquinas ends the first book of the De Caelo commentary:
But according to the Catholic faith, we hold that [the world] began to be, not through a process of generation as from nature, but by flowing from a first principle whose power was not bound to give it existence in infinite time but as it willed, after previous non-existence, in order to manifest the excellence of its power over the totality of being, namely, that the totality of being depends entirely on it and its power is not confined or determined to the production of some given being. Now the things produced by it so as to exist forever have the potency and power to exist forever, and in no way at some time not to exist. For as long as they did not exist, they had no such power; but when they now exist, they have no power with respect to non-existence in the past but to the existence which now prevails or will be - for potency does not look to the past, but to the present or future, as the Philosopher says. Thus it is clear that the preceding arguments in no way impugn the judgment of the Catholic faith.
I think, incidentally, that the same points show that there is no quantifier shift fallacy in the argument. Like I said, I think the hard part is figuring out the arguments for why 'ingenerable' and 'indestructible' are coextensive and why 'generable' and 'destructible' are coextensive, which, although not explicitly mentioned in the argument, is essential to the notion of necessity being used; once that is assumed, the argument follows in strict succession.
