Largest tire size on 2011 LTZ

[Lane]

getting a new set of tires and was wondering what the largest (mainly tallest) tire I can fit on my 2011 Tahoe LTZ 2wd with 20" wheels is. Also if anyone has any input on a good set of tires to get please let me know. Looking for around $800

 

[Boyntonx2]

31" stock
33" leveled

 

[BlkYukon]

The stock 275/55-20 is 31.9" inches