Augmented SkewbA Skewb with additional piece but still only two functional layers per axis.
Circle DinoCould be treated as a slices only variant of a higher order skewb.
Circle GigaminxA Gigaminx with circles that make the visible three piece types hidden earlier.
Circle SkewbA corner turning hexahedron with three logical layers. It looks as if "circle moves" were added to the skewb.
Crazier FloppyA Floppy Cube with a circle that contains hexagonal prism.
Crazy 1x2x3 IIA crazy 1x2x3 with circles on the 1x3 sides. One circle is moving, the other is fixed.