The Master Skewb could be viewed as a combination of three puzzles. The first is the regular Skewb. The second is the Dino Cube. The third does not exist yet, but would be a cube which only contains the M.S. outer centers. A single turn on this puzzle would move nine pieces, so for lack of a better term, let's call it the Nonet Cube. I imagine a cube that looks like a 2x2, but turns around corners weirdly, although I also imagine this would be impossible to build without some seriously crazy tricks.

Then...

Master Skewb - Dino Cube = Skewb + Nonet Cube = Dreidel Skewb
This one has been made.

Master Skewb - Skewb = Dino Cube + Nonet Cube = ?
This would have 8 pieces per face, which could be placed in a pattern similar to a Brilicube. "Briliskewb", perhaps?

Master Skewb - Nonet Cube = Skewb + Dino Cube = ?
This would have 9 pieces per face. It could be made to look like a 3x3 cube (although this would be very difficult), or some other shape (for example, a Skewb with additional Dino edge-pieces at those points that overhang during turns). Either way, the obvious name, "Dino Skewb" is already taken...