An interesting possibility just occurred to me, namely: combining pieces from Rubik's UFO and the Square-1 to create a Star Prism.
Possibility 1: Take the corner pieces from the Square-1 and graft them onto the pieces of the UFO to produce a puzzle that looks like this one: http://www.twistypuzzles.com/large/00775-01.jpg
There would be no restriction on how this puzzle could move.
Possibility 2: Do similar to before, but fuse the two layers of the UFO together to produce something like a star-shaped Rubik's cheese. Then take the rails from the Square-1 and affix them to the pieces similar to how Ton is constructing the 3x3x5. http://www.speedcubing.com/ton/3x3x5.htm
Then add Square-1 corners to the upper and lower layers to produce a 3-layer Star Prism that can turn along all three cuts through the center layer. It would look like this one but wouldn't have the restrictions on movement. Also, the center layer could be the same thickness as the top and bottom. http://www.twistypuzzles.com/large/00625-01.jpg
Possibility 3: Take the puzzle created in Possibility 1 and add the Square-1 rails to it like in Possibility 2 to create a 4-layer Star Prism.
I don't have the means to construct any of these, but if someone else wants to use the idea, go right ahead.