They only puzzle that comes to mind is Eric Vergo's Ultra-X viewtopic.php?t=19090
It has hexhedral, octahedral, and rhombic dodecahedral axes systems. But it doesn't strictly fit your requirements of being a platonic solid because it's a cuboctahedron not a cube or octahedron so it's a shape mod of what you want.
If you do want more shape mods, I suppose you could include a couple of the Dayan Gems, Clay n Eva's Concept 11
, and Eitan's Comboctahedron
as being shape mods of a tetrahedron.
Tetrahedrons have the advantage that face and vertex turns are basically the same so they should be easier to make. I can't think of any non shape mods that fit the requirements, but that could just be my memory failing me.