With some countries considering a fourth booster shot amid the waning effectiveness of COVID-19 vaccines, the European Union’s top health agency is warning that getting boosted ever four months could harm the immune system’s ability to fight off the disease.

The European Medicines Agency advised countries instead to mirror the seasonal influenza vaccination strategy tied to the onset of the cold season, Bloomberg News reported.

In January, Israel became the first nation to administer a fourth shot, targeting those over 60.

The EMA’s head of biological health threats and vaccines strategy, Marco Cavaleri, spoke at a press briefing Tuesday.

“We need to think about how we can transition from the current pandemic setting to a more endemic setting,” he said.

A pandemic becomes endemic, like the common cold or flu, when it becomes seasonal and more manageable as a population gains immunity.

The World Health Organization said in a statement Tuesday that a vaccination strategy based on repeated booster doses of the original COVID-19 vaccines is unlikely to be appropriate or sustainable.

A recent study by Danish researchers found that after 90 days, the COVID-19 vaccines will make you more likely to get infected from omicron, not less.

The New York Times reported scientists were warning that the Israeli government’s recommendation of a fourth vaccine dose to address signs of waning immunity a few months after the third shot could backfire. The scientists said, in the Times words, that “too many shots might cause a sort of immune system fatigue, compromising the body’s ability to fight the coronavirus.”

White House coronavirus adviser Dr. Anthony Fauci, in a March 2020 interview with Facebook CEO Mark Zuckerberg, warned of possible harm from people who get infected with a virus after having been vaccinated.

Last week, a German government study found more than 95% of reported cases of the omicron COVID-19 variant in the country were in vaccinated individuals.

On Monday, Pfizer CEO Albert Bourla acknowledged that two doses of the vaccine his company produces with BioNTech “offer very limited protection, if any” against the dominant omicron variant.

Adding a third dose, he said in an interview with Yahoo Finance, provides “reasonable protection against hospitalization and deaths.”

“Against death, very good (protection), and less protection against infection,” the Pfizer chief added.

In a separate interview Monday, with CNBC, Bourla said the current COVID-19 mRNA vaccines “don’t have the safety profile that we hoped we can achieve with this technology.”

He said the pharmaceutical giant is working on a new vaccine “that will cover omicron as well.”

Bourla told Yahoo Finance “we are awaiting the final results” of clinical trials, but “it will be ready in March.”

However, the latest data indicate the omicron may already have peaked in some areas, including in New York City, one month after the first case was identified, Bloomberg News reported Monday.