At a sprawling Whole Foods Market in Philadelphia, a battle is brewing. The roughly 300 workers are set to vote on Monday on whether to form the first union in Amazon’s grocery business.

Several store employees said they hoped a union could negotiate higher starting wages, above the current rate of $16 an hour. They’re also aiming to secure health insurance for part-time workers and protections against at-will firing.

There is a broader goal, too: to inspire a wave of organizing across the grocery chain, adding to union drives among warehouse workers and delivery drivers that Amazon is already combating.

“If all the different sectors that make it work can demand a little bit more, have more control, have more of a voice in the workplace — that could be a start of chipping away at the power that Amazon has, or at least putting it in check,” said Ed Dupree, an employee in the produce department. Mr. Dupree has worked at Whole Foods since 2016 and previously worked at an Amazon warehouse.

Management sees things differently. “A union is not needed at Whole Foods Market,” the company said in a statement, adding that it recognized employees’ right to “make an informed decision.”

Workers said that since they went public with their union drive last fall, store managers had ramped up their monitoring of employees, hung up posters with anti-union messaging in break rooms and held meetings that cast unions in a negative light.