I believe the guideline is no more than 3/32 difference between current and new to avoid problems.
Last time I bought tires at the dealership, they beat Tire Rack's price. Just make sure they price match and charge reasonable install.
Tire Rack also used to have a service to shave a new tire to a certain depth. I'm not sure if the still offer it or if it only applied to certain tires, but worth researching if you're over 3/32 off.
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