I've always not been terribly impressed by siamese cubes- whilst I can see the appeal from a collector's standpoint, from a solving perspective they've always seemed like just two bandaged cubes banged together. I've always wondered why they couldn't swap pieces between each other, and inspired by Oskar & Tony's reality-bending four-cube puzzle, this popped immediately to mind-

http://www.nebagram.co.uk/C268.jpg

Basically, two fully functional 3x3x5s joined in such a way they can exchange pieces.

Of course if this has been done before/is completely unfeasible/my handwriting is ghastly enough to put you off, feel free to ignore me. I won't mind.

Would it change shape?

I've spent the last hour or two just staring at your picture and messing about it cad. But I stil can't get anything out of it.

The problem with your idea and puzzles in general where the same piece will serve as diferent parts depending on where it is in the puzzle is that if you combine all pieces it is meant to serv as you end up with a part that has no mech left because the mecanism for place A is never the same as B. Which means that when you turn the puzzle with all parts in A-mode the pieces has to let go of the B-mech and vice versa. So if the part ain't conected to neither A or B it simply has nothing that keeps it in place. So the puzzle can't hold it self toghether.

Let me make an example for your idea.
Take the top layer edge on the middle layer of 3x3x5 A, turn this layer 180 degrese and the same part is now in the place were you have the 3x3 corner(the part under the 3x3x5 corner) of 3x3x5 B.
The picture below shows both of these parts rotated in the way they will sit in your puzzle. I tried to intersect these but my cad didn't allow me to, so use your imagination for this one. What you will end up with is a part which has basacly no mechanism atatched to it at all. You can put in the parts that was exluded (mostly the mechanism). But in order for the part to rotate in both ways it can't be atatched to the mechanism.

I allso tried to design this puzzle in a much smaller state, 2x2x3. But I still can't get around the problem with parts having 2 difernt mechanisms.


Did I make any sence at all?

And if you want it to shapeshift, which is possible in the theory.

I won't even try to figgure it out

I think I know what olz means. On a 3x3x5 pieces of the top and bottom layer have a different path if a 3x5 side is turned (large circle performed) as if a 3x3 face is turned (smaller circle). They always do a certain path along a certain axes though. In your design pieces would perform a large circle on one side of the puzzle and a small on the other IN THE SAME DIRECTION/WAY. Or in other words around the same axes (actually not the same but one that is parallel to the other but with an offset.)
So it's definetely not possible by just fusing two 3x3x5 in any conventional siamese-cube way.

I drew a really silly diagramm:



It's supposed to be the same perspective as the top middle picture in your drawings (3x3 face turned 45°)

the black circle is the 3x3 path, the red one is the 3x5 path. The green edgepiece (drawn like a common edge piece) would have to be shaped in a way it matches both, which doesn't seem to be possible, because when the left 3x3x5 face is turned according to the blue arrow/axes it would be on the black circle or the red one in the back of the puzzle.
Btw, I know the grey box (3x4 pieces) doesn't match a 3x4 ratio and that even though it would actually have to be longer to be symmetrical to the big circle.