In the image you see the first score has a piece title which has not been
adjusted, the second one is. The reason why the piece title is colliding, is
because it is aligned to the music, not to the clef.
in my project here, I use lot's of small parts of music, and they're
numbered using "piece" in each header of each score.
The "piece" title seems by default to be aligned in height to the
highest note, which causes the piece title to collide with the clef when
the music is going into the lower regions.
I can adjust it using markup, and \raise, but is there a more general
way to fix it, for example by telling lilypond somehow to align the piece
title to the clef instead of to the notes?