What is the plural of "Starbucks"?
Solution 1:
"Starbucks" comes, as far as I know, from the possessive, i.e. "Starbuck's Coffee", as it was named after the character Starbuck from Moby Dick. With that in mind, it makes sense to me to use "Starbucks" as that would be the same as the plural possessive.
However, I know I've heard "Starbuckses" plenty in conversation. So as far as Southern American usage, that seems fine.
Solution 2:
Starbucks is the name of a company. You didn't see three major corporations on the corner, but three Starbucks stores. So here, Starbucks is more of a description than a noun. Yes, you elide out the "stores" for convenience but that doesn't make it an appropriate noun.
If you saw three stores painted blue, you wouldn't be worried about if you should say that you saw three "blueses" at once. You would just say I saw three blue stores and be done.