San Francisco’s proposed ban on stores and services requiring cashless transactions is expanding to cover Amazon Go stores and Nestle-owned Blue Bottle coffee shops.

Supervisor Vallie Brown’s original legislation exempted Amazon.com Inc.’s cashless convenience stores from the ban on requiring customers use a credit card for food, goods, and services. Brown said the changes were prompted after talking with colleagues and the community.

“Companies like Amazon and Nestle, owner of Blue Bottle, are making record profits. For the second year in a row, Amazon will not pay federal income taxes on $11 billion in profits. They can afford to hire...