31's will rub even with the budget boost. stock, you stuck with stock tires, you might be able to up size a little (completely made up number but like 235-70r16 tires to 235-75r16) but nothing noticable.
with the fancy pantsy 4" lift, 33's is the max tire that is advertised to fit, that said, there is 1 liberty in my club that has 35" tires, but it has a 100% custom lift and Solid front axle, lots of bumper trimming.
the biggest issue with liberty's is the wheel wells are so damn small, and they do not lend themselves to being easily trimmed.