Defining the role of a critic remains always a negotiation between possibility and impossibility. Based on the readings of Dryden, Coleridge, and Elliot, examine how they negotiate such concerns in their different approaches.

All three of these men wrote both poetry and criticism (or expressed critical opinions in their poetry) during periods of transition in English literature and in Western literature overall. If I understand your question correctly, you are asking about "possibility and impossibility" in relation to a literary critic's ability to express views that are definitive, that express an objective judgement that will have validity for other people, and that will still be valid beyond the critic's own time and his own immediate concerns. Is this, in fact, possible, and did those particular writers achieve this?
John Dryden wrote at a time when the English were first recognizing their own greatness as a literary nation. In expressing his critical views he drew a distinction between, on the one hand, poetry he believed was of universal significance and could transcend its own time, and on the other, poetry that may have had value at one time but was now stylistically out of date. Though tastes had changed radically over the past half a century, Dryden regarded Milton as not only the greatest of English poets, but the greatest epic poet in history, surpassing Homer and Virgil:

Three poets, in three distant ages born, Greece, Italy, and England did adorn. The first in loftiness of thought surpassed, The next in grandeur, and in both, the last. The force of Nature could no farther go: To make a third, she joined the former two.

On the other hand, Dryden regarded John Donne as a poet whose affectations prevented him from achieving true greatness:

He affects the Metaphysics in his amorous verses, where nature only should reign; and perplexes the minds of the fair sex with nice speculations of philosophy, when he should engage their hearts.

This is where the designation of Donne and others of his period as "Metaphysical" poets began (and was more fully developed by Samuel Johnson nearly 100 years later). Was Dryden correct about Milton and Donne? Was it possible for him to judge the poetry of his own century in a way that would be valid for the future, up to our own time?
S.T. Coleridge, in his Biographia Litteraria and in his critical writings in general, was far more comprehensive than Dryden and perhaps any earlier English critic in setting down his ideas about the aesthetics of literature. Interestingly, however, though both Coleridge and his friend Wordsworth were in the forefront of the Romantic movement, in many ways their aesthetic and critical views were diametrically opposed. In chapter 18 of Biographia Litteraria, Coleridge takes issue with Wordsworth's ideas about something as fundamental as the appropriate diction for poetry, which Wordsworth had dealt with in the preface to Lyrical Ballads—a volume that contained poetry by both men—some fifteen years earlier. Though both Wordsworth and Coleridge are among the most important of all literary critics, did each one express views that continued to be valid beyond the Romantic period?
T.S. Eliot's writings on poetry are problematic because, although he was one of the leaders of the school of criticism known as the New Criticism, many of his views were eccentric and were no longer taken seriously by scholars soon after Eliot's death. Much of his critical writing is deliberately iconoclastic, unsurprisingly so in an age (the early twentieth century) when there was a huge reaction against the aesthetics of the Romantic and Victorian periods. His early essay on Milton was scathingly negative. For over two hundred years, beginning in Dryden's time, Milton had held an iconic status in English poetry. Eliot (in his first essay on Milton—he later moderated his views) and his followers such as the professor and critic F.R. Leavis attempted systematically to dismantle Milton's status while simultaneously building up Donne and the other Metaphysical poets who had been largely ignored for nearly 300 years. Eliot also expressed an iconoclastic view of Shakespeare, regarding Hamlet an inferior play and asserting that Shakespeare's greatest achievements in tragedy were Antony and Cleopatra and Coriolanus. Some would say that Eliot put forth these opinions in an arrogant, derogating manner, as if to say that anyone who disagreed with him (which, in fact, would be most of the world regarding Hamlet) was a fool.
One can look at the diversity of views expressed over a period of 250 years by Dryden, Coleridge, and Eliot and ask: is it even possible for a critic to establish objective standards about literature? Most critics, including these men, tend to voice their ideas with the kind of boldness that ignores the fact that, regarding literature or any of the arts, it all comes down to opinion—to what the critic himself, or herself, thinks. But is it even necessary to make this point explicit? Is it incumbent upon us, as readers, to acknowledge that of course, whatever a critic writes is merely his personal view, and that other views are valid? I tend to think that the three critics in question, simply by virtue of the fact that we're still reading their criticism today, did "negotiate" the region between the possible and the impossible with as much skill as any writer is capable of applying to this very difficult and problematic issue.