The phrase 'possibly great' is correct and usable in written English.
You could use it when you have a feeling that something may have the potential to be great, but you are not certain. For example, "I think this movie may be possibly great."
A possibly great opportunity lies ahead for the human race.
We have one possibly great player, wonderful Wayne, but he seems not to be able to "do it" in the big games.
There are times where it can be useful (if you're going to a city with limited restaurant-review options, Zagat can steer you to a place that will probably be just fine, and possibly great), but what Zagat used to have to itself has become its own industry with plenty of competitors.
And to judge by the hosannas the show has inspired ("marvelous, possibly great, art," The New Yorker said), beauty of a certain kind — familiar, object-based, museum-ready — is what certain viewers need from Mr. Hammons now, so that they can finally assign him a spot in the post-everything — post-race, post-class, post-politics — canon of greatness.
Certainly the wild success in both forms explains why this is one distaff story Hollywood can get behind: even as the final Swedish movie brings the initial screen cycle to a close, David Fincher is directing the first American adaptation, a sign that a good, possibly great screen version might still happen.
Why would any serious investor tie his financial decisions to information produced by accountants who know that there little risk (at least in the short term) and possibly great reward in putting forth doctored figures and in concealing bad news about the corporations they serve?
Possibly greater expense, too, and not just for the wealthy.
Without Boswell's artistry, Johnson's genius, though possibly greater, would scarcely be alive for us.
Beyond those arguments, fisheries experts say, is another, possibly greater, ecological collision, not far away.
Possibly, greater exclusion criteria are needed than currently recommended for the use of buproprion at therapeutic doses.
Dostoevsky's last, longest and possibly greatest novel has been known for nearly 130 years in English as The Brothers Karamazov.
