Science says they could! A song is just a soundwave with a particular pattern.
A different song has a different soundwave with a different pattern.
If you combine the two songs, you get just one soundwave!
One mouth, one soundwave, two songs! Could a singer perform such a feat? A superhuman one, perhaps.
While not typically performed by a lone singer, combining multiple different melodies into one is a real thing in the world of music called a polyphonic texture. For a real life example of this technique in use, check out the end of Disney's "We Don't Talk About Bruno" from Encanto, where all the various singers sing their part of the song all at once.