Pfizer Inc and BioNTech SE said on Thursday they are testing a third dose of their Covid-19 vaccine to better understand the immune response against new variants of the virus.

They are also in talks with regulatory authorities about testing a vaccine modified to protect specifically against the highly transmissible new variant found in South Africa and elsewhere, known as B.1.351, as a second arm of the same study.

The companies believe their current two-dose vaccine will...