What is the maximum number of spheres that can be placed in 3D such that all inter-touch?

One can of course place four unit spheres tetrahedrally and then add a smaller sphere in the middle, so this number must be at least 5.

[By the way, I was trying to extend the "five points in 2D cannot be inter-connected without a crossing" limitation to 3D with a simple statement, but this was sadly the best I could do. If anyone knows a better simple extension, please comment.]