You might view this riddle on my prefix,
It also comes with cheese,
My infix is the largest of my suffix,
I am a cunning scheme.
What am I?
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You are a
MACHINATION: machine, China, nation. I confess I'm not sure I understand the bit about cheese. Largest by population, of course.
EDITED to add:
Some astute commenters point out that instead of viewing this on a machine you could view it on a Mac -- and then you have both the "big Mac and cheese" (a cheeseburger) and "mac and cheese" (a pasta dish). Thanks, @noedne and @MichaelMaggs!
Mouse: mice eat cheese, and we may be viewing this with a mouse (computer)