Unfortunately I would expect that this would be impossible based on considerations of the energies involved. While it may be true in some sense that matter is actually made up mainly of empty space, it would cost enormous energy to create open passages in it. Here's a couple of ways one could imagine doing this:
* We could keep the atoms more or less intact but pushing them closer together in places to create passages of some sort.
* We could go inside the atoms and push the electrons off to one corner or closer to the nucleus or whatever.
Doing this would cost huge energies, of order electron volts per atom. The atoms in a solid sit where they do because that minimizes energy spent. If you start moving atoms around by pushing some of them closer together, the energy goes way up. The electrons in an atom are in orbits because that is their lowest energy configuration. Forcing them into a small region again pushes the energy way up. The size of energies that we are talking about are roughly the same energies that it would take to vaporize the solids. You might want to think about how to pass a solid object through a block of ice. You could always do it by heating up the ice enough that it turns into water or steam passing the solid object through and then refreezing the steam or water (assuming that it hasn't dispersed in the meantime). This example raises another issue. At least one of the objects involved is this process, assuming enough energy was available for them to somehow pass through each other, would likely be mangled beyond recognition (basically broken down into individual atoms as in a gas state) after the process was finished. This is starting to sound a bit like "beam me up Scotty" in Star Trek. One perhaps imagines that the human bodies are disassembled for the transportation process and then reassembled afterwards. How you get them back together the right way is difficult to imagine! 24