Cooper ST Maxx - how big can I go?

I have a stock 2017 TRD Off-Road and need new tires - like now. I am newish to the 4x4 world and want to get more off-roading in my life. I am planning a lift in the next year or two but can't wait until then to replace my shitty tires. I am seriously looking into the Cooper ST Maxx. Any recommendations on how big I can go with standard rims and still avoid too much rub? Don't need mud flaps. Thanks!

 

255/85r16

 

https://www.tacomaworld.com/threads/put-255-85-16s-on-stock-or-wheels-and-suspension.491079/

Might even decide after running them you don’t need a lift at all...

More reading https://www.tacomaworld.com/threads/255-85-r16-owners-experience.155849/