(CBS News) — More than 34 million Americans age 50 and older could soon be eligible to receive another booster shot, after the Food and Drug Administration said Tuesday it had authorized a new round of the Moderna or Pfizer and BioNTech COVID-19 vaccines for those who want them.

The Centers for Disease Control and Prevention must also sign off on updated recommendations before providers can begin giving the extra boosters.

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“Current evidence suggests some waning of protection over time against serious outcomes from COVID-19 in older and immunocompromised individuals,” said the FDA’s Dr. Peter Marks said in a statement.

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So far, only Americans with compromised immune systems have been eligible to receive a fourth shot if they were first vaccinated with the Pfizer-BioNTech or Moderna vaccines, or a third shot if they had initially gotten Johnson & Johnson.

Americans who are old enough to be eligible will be able to get the second booster as early as four months after their first booster. Immunocompromised Americans ages 12 and older who were boosted will also be able to get another shot.

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