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The phrase "a slightly different set" is correct and usable in written English.
It can be used when referring to a variation or alternative group of items, options, or elements that are not entirely the same as another set.
Example: "In this experiment, we will analyze a slightly different set of data to see if the results vary."
Alternatives: "a somewhat altered group" or "a marginally distinct collection".
Exact(57)
Filing during the summer has a slightly different set of eligibility requirements.
More than 300 such accords already exist, each with a slightly different set of rules.
High-end food was, ultimately, still high-end food, just with a slightly different set of techniques.
Similarly, we pull together a slightly different set of stories on the weekends to avoid the headlines becoming stale.
All these things and a myriad more combine to give every person a slightly different set of advantages or disadvantages.
Every time a patch is replaced, users must readjust: small changes in location means that it picks up signals from a slightly different set of muscles.
Each of them operates from a slightly different set of assumptions about the world, their industry, what can or can't be done.
The United States imposed the ban in March and was quickly followed by Britain, which imposed restrictions on a slightly different set of routes.
Similar(3)
Algorithms use existing data to make predictions about what might happen with a slightly different setting, population, time, or question.
By now, Mr. Frank was growing so frustrated at seeing so many unsuitable places that this one seemed like a "happy medium in a slightly different setting".
"It was a slightly different set-up, with different people working on each part of my training, and it was good," Murray said.
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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