So in terms of crossing number https://arxiv.org/pdf/1808.10480 gives a lower bound of $O(e^{2.5}/n^{1.5})$ for multigraphs with no face of length 2 with no node contained inside. What do we know about the pair crossing number for multigraphs? (The pair-crossing number pair-cr(G) is the minimum number of crossing pairs of edges over all drawings of G)
Also what is known about the largest number of other edges crossed by an edge of a dense multigraph.
