Several more of the country’s most ubiquitous retail chains said this week that they will ask customers to refrain from openly carrying guns in their stores. The requests, days after Walmart announced a similar policy, marked a notable shift in the debate about the presence of guns in everyday life in the United States.

In a short statement posted Thursday, CVS Health requested that customers, other than authorized law enforcement personnel, do not bring firearms into its 9,900 stores in the country. Walgreens, with 9,500 stores, did so as well. Both chains noted that they were joining other retailers. Wegmans, a supermarket chain with 99 stores mainly in the Northeast, noted its request on Twitter.

“The sight of someone with a gun can be alarming, and we don’t want anyone to feel that way at Wegmans,” the tweet said.

As private entities, the retailers have the right to restrict guns in their stores. But it remained unclear how they might compel customers to comply, and the policies were framed as requests, not outright bans. Several other large chains have enacted similarly worded policies over the last several years, including Starbucks, Target, Costco and Chipotle.