Starbucks is big enough they could probably switch over to completely reusable coffee cups and cause the industry to follow. Bring a reusable cup and get your coffee like normal. Forgot yours? You can buy one at or slightly above cost along with your coffee.
Risks to address:
People treat the reusable cups as disposable anyway. I don't see a *massive* chance of this happening given the financial incentive to not do so. But maybe have a discount program where returning used cups also reduces the cost or fills your Starbucks account.