"in all its variations" is correct and usable in written English.
You can use it to refer to the different ways in which something can be expressed or experienced. For example, you could say: "This style of art has fascinated onlookers in all its variations for centuries."
And when it comes to sex, in all its variations, Victorian writers – who tended to be drawn from the more progressive bit of the middle-class – were determined to explore the full range of experience.
The typical Taylor Swift song is gentle but full of insistent hooks; it features Swift's delicate voice, singing about love in all its variations — or, as she told me, "Love, and unrequited love, and love that didn't last, or love that you wish had lasted, or love that never even got started".
In fact, indigo in all its variations is St.-Tropez's most popular shade.
The Boeing 777, in all its variations, is one of the safest aircrafts ever built.
Nettle and wild garlic soup Nettle soup in all its variations is a springtime favourite at River Cottage.
Finally, there is the simplest argument of all, that life itself, in all its variations, is astonishing and mysterious, and that humans have a responsibility to preserve it.
Now, as the world mourns the loss of a talented, tortured man, the sum of that work in all its variation takes on a different kind of sweetness.
And although Donald Trump is by all other accounts a grown man, he reduces politics to the point of complete distortion, hopeful that his policies will appeal to those who, like he, have no experience thinking critically about the complexities of what it means to be not only the president of the United States, but a defendant of democracy and humanity, in all of its variations.
Yet here is life in all its unvarying variations.
The fate of allegory, in all its many variations, is tied to the development of myth and mythology.
The vocabulary of unrest is present in all its characteristic variations: the alienated air of hauntingly ambiguous cast-bronze figures leads to attempts at abstract transcendence, painstakingly carved from marble and alabaster.
