The phrase "with variants" is correct and commonly used in written English.
It is typically used to refer to different versions or options available for something, typically within a specific context. Example: "The product comes with variants of colors to match every individual's taste."
Some people are working with variants of the stealth theory.
Richard Tuttle, Jonathan Lasker and Andy Warhol go wan, with variants that are respectively cerebral, institutional and chic.
In New York, such pooled funds are staples of Trinidadian immigrant communities, and, with variants, of many other immigrant groups.
They turn to each other, friends and strangers alike, with variants on the same question: Is this for real?
Whenever I write about global poverty, I'm deluged by readers with variants of a single question: What can I do?
Man cannot act alone, even when he has just the one character to perfect (with variants: moody sparkly emo teen and moody NOT sparkly emo teen).
But Esther cannot read or write, and thereby hangs a tale with variants extending from the Puritan John Alden to Cyrano de Bergerac.
He was the first Arab barber in Brooklyn, he says, pulling out a contact sheet of photos of his customers, all with variants of a stylized buzz cut.
Yankee fan websites are abuzz with variants on the theme that Steinbrenner had clung to life to wait for Sheppard to announce his arrival in heaven.
Baldwin of course, established the form with variants of "I'm gonna fuck you up," delivered free-style in the street to reporters and photographers.
His company has compiled a searchable database of about a billion names from all over the world, with variants, cultural and ethnic identifiers, and chief countries of origin.
