The only way I know is to have the session "run" so that it's (say) 2 songs, 2 tunes, turnabout..

But it does happen at sessions. Tends to happen when there are more fiddlers than singers. The trick is to help them realise that the voice is an instrument too, and that just because you're not diddling away at a tune, you might nevertheless be ready to start...

Good Luck....

:-)