The phrase "acknowledged not only" is correct and usable in written English.
It can be used when you want to emphasize that something has been recognized or accepted in multiple ways or contexts.
Example: "The committee acknowledged not only the efforts of the volunteers but also the contributions of the sponsors."
Alternatives: "recognized not just" or "accepted not only".
But Lillian's superhuman qualities are acknowledged not only by Gabriel but by everyone else in the novel.
He acknowledged not only selling fake paintings and misrepresenting their origins to customers, but to painting many of them as well.
Yet, even as Mr. Navalny and his aides lugged 21 boxes of documents to the courthouse, they acknowledged not only that there was little hope of overturning the results, but also that the voting had been relatively fair.
In the course of many pre-trial hearings, both the defense and the prosecution have acknowledged not only that the first phase will be short but also that its outcome is all but preordained.
More than that, it would go on to permeate modern consciousness and art, acknowledged not only as a sneering, overused pose of detachment, but also as a potent weapon for delineating a fractured and frightening world.
By outing the importance of dramatic history in his work, he acknowledged not only where he was coming from but where he needed to go: deeper into the idea of theatre as artifice.
Ms. Franklin made a point of acknowledging not only her birthday — she turns 66 on Tuesday — but also Easter.
The audience can acknowledge not only the gay people onstage but also the gay people in the seats around them.
Before we declare this a moment of unprecedented concession, we should acknowledge not only the history of self-censorship but also ongoing censorship in Hollywood.
Christians acknowledge not only a duty to announce the gospel, profess the faith, and worship God but also to live their entire lives according to God's will.
"The Science of Getting Rich" is a self-help book, but it is also a political manifesto: it urges its readers to acknowledge not only the importance of wealth but also the arbitrary nature of its distribution.
