Based off of what I have read of other people's experiences, the following is what I think I know but I could be mistaken.
Its hard to give an exact answer because the backspacing of your wheels makes a huge difference in clearing (or not clearing) the lower part of the front spring perches, and in having room at the front side of the bottom of the rear fenders (plastic liner).
Trailhawks comes with a roughly 28x8.5 tire, staying under 9 inches wide that slightly narrower tire helps avoid that front spring perch in trade for the height. Then there are some top trim Limiteds and High Altitudes that have the optional 19 inch rims they use more like a 27x9.3 tire so they go shorter to stay well under the spring perch and have room for the wider tire. And your current rims split the difference at about 27.5x8.9.
So "biggest" really depends on whether you are talking about width or just height. On a 215 profile you can probably clear the spring perches and fender liners with a 29 inch tire but it will have to be skinnier than the ones you have now. Or by "bigger" you could go much wider but might have to lose a half inch of height to again clear spring perches.
If you search around the forum you will find various tire sizes people are fitting but you have to pay attention to whether they are talking 1st gen or 2nd and whether their rims are stock or if they changed to rims with more backspacing, or whether they used spacers, etc. Fun fact, a lift alone doesn't really change the size of tire you can fit most of the time because its still a spring perch clearance issue in the front before you run into problems hitting the fenders but its a close race.
The only people who seem to fit 30 inch tires end up going spacers and lift both. 29 inch like I said kinda have to stay with a skinnier tire or get spacers. 28 should fit stock even at a 235 width potentially but it may be close on those perches. Search the site for other people's setups to confirm.
Thank you for your insight. Glad I came upon this thread because I'm currently in the market for replacement tires. There's this m/t tires that caught my attention, but I'm not exactly confident that I'll get the right size without rubbing. I'm also planning to get my rig lifted for the first time at least 3" so I have to review and ask my mechanic what to do about it.
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