U.S. officials have said they expect Covid-19 booster shots to be available for more people beyond the immunocompromised later this month. Some aren’t waiting.

Eager booster seekers are crossing state lines, listing autoimmune disorders they don’t have on pharmacy forms and asking healthcare workers to bend rules. Those looking to get the additional shots as soon as possible cite factors including the high transmissibility of the Delta variant, the new school year and some employers’ return-to-office plans.

Julie Levitt said she told a clerk at a Publix Super Markets Inc. pharmacy that she and her fiancé were immunosuppressed when they went in for a third shot of the Pfizer vaccine recently. They aren’t. The 51-year-old personal assistant in Orlando, Fla., said the couple wanted to boost their immunity against Covid-19 ahead of their wedding in a few weeks. She said the clerk didn’t question her request. Minutes later, she received the shot.

“I don’t think they care” about people’s motivations for getting a booster, she said. “There are so many vaccines now, and nobody is getting them.”

Daily vaccinations have risen in recent weeks as people seek out protection against the Delta variant and officials redouble efforts to raise inoculation rates. Some 61% of eligible people in the U.S. have completed their initial Covid-19 vaccination regimen, according to Centers for Disease Control and Prevention data, leaving millions still in need of shots. Federal officials have said ample supplies of authorized vaccines would be available to give booster shots to people who are eligible.

The Biden administration announced that Americans who have been fully vaccinated with a two-dose regimen against Covid-19 should receive a booster, citing the threat from the highly contagious Delta variant. WSJ breaks down what you need to know. Photo: Hannah Beier/Reuters The Wall Street Journal Interactive Edition

The Food and Drug Administration has authorized boosters of the Pfizer Inc.-BioNTech SE vaccine or the Moderna Inc. shot for people with compromised immune systems. Approval of boosters is expected as soon as mid-September for eligible people who received a full regimen of those drugmakers’ two-dose vaccines months ago as well as for Johnson & Johnson’s single-dose shot.

A lawyer in Illinois said he crossed state lines to get a booster at an independent pharmacy in Wisconsin, correctly guessing that it wouldn’t check an Illinois database that listed him as having received two shots. He said he decided to get the extra dose before he is eligible because his new employer was encouraging him to return to the office without requiring vaccination or masking.

“‘I’m trying to be as careful as possible to keep them protected and myself protected.’”

— Elliot Berg, a Texas father, referring to his children

Some booster seekers said they have gotten an additional shot without any extra effort.

Elliot Berg, a 46-year-old real-estate developer, said he visited a vaccination clinic last week in an office building 2 miles from his home in El Paso, Texas. He wrote on the required form that it would be his third shot.

“Thirty minutes later I walked out with a sore arm and a headache,” he said.

Mr. Berg said that he isn’t immunocompromised but has asthma and travels frequently. He said he also worries about keeping his three children safe. Vaccines are currently approved in the U.S. only for people ages 12 and over.

“I’m trying to be as careful as possible to keep them protected and myself protected,” he said.

People waited for observation after receiving booster shots in Southfield, Mich., on Aug. 24. Daily U.S. vaccination rates have risen in recent weeks.

Photo: Emily Elconin/Getty Images

About a quarter of 1,517 vaccinated adults surveyed by the nonprofit Kaiser Family Foundation in July said that news about boosters made them worry they might not be well protected against the virus.

Roughly 955,000 people have received an additional Covid-19 vaccine dose since Aug. 13, according to the CDC. At least 10 million people in the U.S. take immunosuppressants that would likely already make them eligible for boosters, according to Johns Hopkins University School of Medicine.

Peppi Kramer, 61, who takes immunosuppressants for rheumatoid arthritis, said she easily got an appointment for a third dose at her local pharmacy—unlike earlier this year when she joined a Facebook group of vaccine “hunters” to figure out how to get a shot. She said she is more worried about people who refuse to get vaccinated than those jumping the line for boosters.

“If someone else wants to sneak in there right now, go ahead,” she said.

Write to Julie Wernau at Julie.Wernau@wsj.com and Anne Marie Chaker at anne-marie.chaker@wsj.com