For Jennifer Woda, two doses of the Moderna Inc. vaccine were not enough protection against COVID-19. Over a month later, she got a third and fourth dose, this time with the Pfizer Inc.-BioNTech SE vaccine.

An opera singer who teaches music to kids, Woda received a kidney transplant in September 2019, one of about 160,000 transplants that have occurred in the U.S. since 2017. Emerging research is now showing that these patients, who suppress their immune system with drugs so their bodies don’t reject donated organs, are dramatically less likely to develop protective antibodies using the authorized vaccine dosage.

That’s spurring some recipients to get extra shots as worries mount over the end of pandemic restrictions and as U.S. vaccine supply outpaces demand. They went to pharmacies and clinics to get their shot on their own without doctor’s notes. Some weren’t asked questions about their vaccination history, and some explained their situation and still got the shot.