Stewart Coffin made one two-tiered triacontahedron and there is a picture of it on puzzleworld's website. Here is the link http://www.puzzleworld.org/PuzzleWorld/toc.asp?t=_des/sc001.htm&m=des/sc000.htm
Then navigate to Design Number 72 (Two-Tiered).
What do the pieces look like? Unknown, at least to me.
I see a large variety of ways you could do this though. You could use a Des 72 on the inside, then cover the outside with a five spoked piece which would be the dissected faces of five sides. Much like the Two tiered R-D, the innner and outer layers would be cut in opposite directions. The outside tier could also be the dislocated Jupiter with its pieces projected onto the faces of a triacontrahedron. Any outer shell pieces would have to be deeply truncated.
You could also use a Jupiter for the outer tier. Or Dislocated Jupiter for the outer tier.
The inner tier could be a Saturn puzzle, that has its pieces projected down onto the faces of the triacontahedron itself.
The inner tier could be Stewart's Venus puzzle (#160). Although the more sequential nature of it may cause difficulties.
The inner tier could be Stewart's Sphinx puzzle, that has its pieces projected down onto the faces of the triacontrahedron.
The inner layer could be the dislocated Jupiter projected down. Which would basically be four spokes from the center and one spoke off of one of the end of those four, all identical.
Then you could get into the fact that the inner tier pieces do not necessarily need to be free standing on their own first before the outer layer is added. This allows for interior pieces in configurations that would fall apart on their own but the outer pieces are the "glue" that hold them together.
I don't think you would be able to incorporate your Chinnyhedron unless it is just a cover for the whole two tiered puzzle or on the inside as a box within the box. If it were physically attached, then the whole puzzle would be a two piece puzzle.
I will send you the scanned images for Des72 and Venus which show the pictures of the pieces. Can also send the Saturn and Sphinx images if you need them.
So above I've listed 4 possible outer layers and 4 possible inner layers, so there are 16 different varieties. If you used any of Wayne's puzzles for the interior then there are even more varieties. In any case, the overall puzzle would be a huge pain in the ass to make and get right. Good luck in your endeavors.
I would like to see your drawings of Pelikan's 4 pc...