The liberal workers the company has long attracted are expanding a union campaign to other cities after a landmark victory in Buffalo.

Maggie Carter, a Starbucks barista in Knoxville, Tenn., is a warm and reassuring presence who says she is keen to “go the extra mile” for customers.

She may also be a nightmare for Starbucks executives.

As a union organizing campaign that began in Buffalo and produced the company’s only two unionized U.S. stores spreads to other cities, it is being driven by workers like Ms. Carter: young, well educated, politically liberal.

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