I have an idea I wanted to share with you. I've searched the museum section and haven't found anything similar and I think it'll be interesting from solving point of view. I have even concept how would mechanism look like.
We all know Crazy Planet Puzzle series. They are basically Rubik's Cubes with circles on each face that either stay fixed or rotate when turning said face. There are few variants having more or less faces with 2 kinds of center pieces allowing each of two types of movement. They are sometimes called 0s and 1s as in the following picture.
My idea here is to allow centers to behave in both ways depending on situation. To achieve this instead 0 and 1-type centers one must have 0 and 1-type edges. When we have at least on 1-type edge on the face that face turns like a normal Rubik's Cube. When there are none of them (only 0-type pieces) it works like Circle Cube.
And here's my concept of mechanism.
Each of the six arms of the core would allow center pieces to rotate freely but would have square sections necessary to block movement when needed. Additionally center pieces would have holes on bottom side for the same purpose.
There's also another piece bellow center piece that change behavior of centers. It's position is affected by near edge pieces. 1-type edge pushes it down allowing Rubik's Cube movement. When there are no such pieces a spring pushes it from the below and makes face rotate like Circle Cube.
All pictures can be seen here
Also if anyone knows a software that I'm not aware of that simulates such a puzzle please post a link here, I'd love to play with it.