The phrase 'may vary depending on' is correct and usable in written English. You can use it when referring to something that could be different in various circumstances or situations. For example, "The cost of the product may vary depending on the location."
(Prices may vary, depending on the event).
This process may vary depending on your software.
Length of incubation may vary depending on assay.
(Closing time may vary depending on the crowd).
Your co-pay may vary depending on the surgical method.
(Prices may vary depending on where the purchase is made).
Computational and control effort may vary depending on selected manifold.
The figures may vary depending on the type of discounts that are available.
The size of the pit may vary depending on the amount of food.
(These steps may vary depending on the version of Windows you are using).
But those dynamics may vary depending on keywords and how carefully advertisers aim their pitches.
Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.
Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com