The phrase "a set of men" is correct and usable in written English.
It can be used when referring to a specific group or collection of men, often in contexts related to teams, organizations, or categories.
Example: "The project was assigned to a set of men who had extensive experience in the field."
Alternatives: "a group of men" or "a collection of men".
It seems to me that I have been abetting an act of frightful wickedness and violence, performed by a set of men against one of their fellows; and I pray God that it may soon be out of the power of any man in England to witness such a hideous and degrading sight".
They're a different class now as a set of men, we're going into every game thinking we can win it.
The only surviving daughter, she considered herself the "odd number in a set of men".
And now we find ourselves watching, as our representatives are reduced to a set of men and women who are also merely watching.
Politicians [are] a set of men who have interests aside from the interests of the people and who, to say the most of them, are, taken as a mass, at least one long step removed from honest men.
This study determined that the lithology of a set of man-made Everglades tree islands played a primary role in regulating the seasonal fluctuation of the water table and hydrogeochemical processes.
Five years ago, as often happened, Ian Nagoski was stuck behind the counter of his True Vine record store in Baltimore one afternoon when a set of burly men showed up at his door carting a box of records.
There are photographs documenting Willets Point, the automotive scrapyard in Queens, and a set of portraits of men whose skin appears as colorful scales.
Fairchild cut the circulation to 400,000 and came up with an editorial formula that appeals to a moneyed set of men and the advertisers that covet them.
A Union prisoner saw the Tigers return and claimed, "A madder set of men I never saw".
A remarkable cast of the company's most senior ballerinas — Darci Kistler and Kyra Nichols (the company's last two Balanchine-era members), along with Miranda Weese and Wendy Whelan — were partnered by a sterling set of men (Charles Askegard, Nikolaj Hübbe, Tyler Angle and Nilas Martins), and they perfectly evoked the work's romantic fervor and heart-wrenching intimacies.
