  Graph drawing beyond planarity focuses on drawings of high visual quality for
non-planar graphs which are characterized by certain forbidden edge
configurations. A natural criterion for the quality of a drawing is the number
of edge crossings. The question then arises whether beyond-planar drawings have
a significantly larger crossing number than unrestricted drawings. Chimani et
al. [GD'19] gave bounds for the ratio between the crossing number of three
classes of beyond-planar graphs and the unrestricted crossing number. In this
paper we extend their results to the main currently known classes of
beyond-planar graphs characterized by forbidden edge configurations and answer
several of their open questions.
