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As long as you are "plus" sizing the tires and wheels (as you increase wheel diameter, you have to shorten the sidewall height to maintain the same overall diameter of the tire - regardless of the diameter of the wheel.
Take 205/55-16 being the OEM size. Jumping up to a 17" wheel, tire would have to be a 215/45-17.
An 18" wheel, tire would have to be a 225/40-18. A 19" wheel, tire would have to be a 225/35-19. Go 20" wheel, tire would have to be 235/30-20. Even then, each manufacturers tread design could influence how much offset there is in the speedo. Keeping with these numbers, generally will yield a 3% or less speedo discrepancies.
Wheel width also can be a factor, running a much wider wheel than recommened can "stretch" the tire. Sometimes this is done on purpose (IMO, a really bad idea from a decade of tire/wheel R&D and forensic work).
On this generation - I'd try and stick to 7"-8" wheel widths, depending on the diameter of the wheel. Any more and you'll likley run into clearance issues with the suspension and/or the body. That point, you'll have to roll the fender and/or run spacers. How much will be dictated by wheel offset.
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2002 Corolla S, 1.8L 1ZZ-FE VVT-i
2003 Matrix XRS, 1.8L 2ZZ-GE, VVTL-i (RIP)
2009 Matrix XRS, 2.4L 2AZ-FE VVT-i
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