"it fits perfectly with" is a correct and usable phrase in written English. It is usually used to indicate that two objects or ideas go together very well. Example sentence: This blue dress fits perfectly with these black heels.
Part of what makes the obstruction strategy so appealing to Republican leaders, along with its supposed ability to kneecap opponents, is that it fits perfectly with the right's ideas about the role of government.
"It fits perfectly with everything we're trying to do here".
"It fits perfectly with the plan," Mr. Milliner said.
The thing I've loved about launching the site is that it fits perfectly with my principles.
We thought it fit perfectly with the campaign".
In the case of Rounder, Mr. Barros said, it "fit perfectly with who we are".
However, Channel 4 defended the show, with head of documentaries Nick Mirsky saying it fitted perfectly with the broadcaster's remit of "producing programming that stimulates discussion and debate, the first series did this on a national scale".
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Maria Pia Montoro
Terminologist and Q/A Analyst @ Translation Centre for the Bodies of the European Union