Yes, you can set NDim, https://graphviz.org/doc/info/attrs.html#d:dim I'm not sure why we said up to 10. It's hard to see even in 8 dimensional space!

In terms of drawing graphs of the U.S. states or data like that, it should be possible to, say, create a point at the centroid of every region, then connect the adjacent regions to form a mesh, then feed the mesh to neato with some options to relax the layout but retain the mesh. This is what the overlap removal algorithm does anyway. See https://www.graphviz.org/Documentation/GH10.pdf, at least the figures.

There's plenty of recent work that improves on some of the graphviz algorithms. It's a pity that without a convenient way to incorporate such inventions in a larger system, it tends to languish and not have as much impact or isn't easily available to people that could use it. Nocaj/Ortmann/Brandes work on untangling hairballs is another example: http://jgaa.info/accepted/recent/NocajOrtmannBrandes.pdf We even have this prototyped in a directory somewhere but it would be more work to merge it into the release.