In France, they started offering a booster dose to some people, such as cancer patients and transplant recipients.
But in the U.S., it's not authorized or recommended.
Doctor Emily Blumberg, director of Transplant Infectious Diseases at Penn Medicine, says there isn't enough research to say if a booster dose for immuno-compromised patients is safe or effective.
"We're still trying to figure out who benefits and who doesn't benefit from that additional vaccine," she said.
A prominent transplant surgeon in New York and heart recipient himself says he got a boost to his antibody level from a third dose.
But studies overseas show some people don't, and it's possible an extra dose could spark rejection of the transplanted organ.
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According to antibody testing, in some at-risk patients, the current vaccine regimen offers much less protection than it does for healthy people.
But Blumberg says that's only part of the story.
"You may have some benefit to the vaccine that can't be measured by antibody, and we call that your cellular response," she said.
So far, the majority of people winding up in the hospital now have one thing in common.
It's not a compromised immune system but an unvaccinated one.
Blumberg thinks two things are helping protect the vulnerable.
"We suspect that both their own vaccines and very importantly, the vaccinations of those who are around them are protecting them from getting really sick," she said.
Blumberg says if you have a suppressed immune system, you should take extra precautions just in case.
That means avoiding crowds and continue wearing a mask when indoors when you don't know if people around you are vaccinated.