Online since 2002. The most comprehensive site for all around twisty puzzles.

Cubes with interchangable pieces
4CubesFour parts (looking like a 3x3x3) connected into a single puzzle.
Cubes on a DiskTwo 4x4x4 connected with a disk which allows to exchange pieces between the puzzles.
Cuboids on a TorusFour Cuboids connected together on a torus which allows to exchange the pieces between the puzzles.

HATO PuzzleThe first physically implemented 4D cube.
Seven Star UFO7 spherical 2x2x2s embedded in an UFO-like shape. The pieces can be exchanged.
Swap CubeFive differently colored 2x2x2 embedded in a strange mechanism which allows one to exchange the cubies between the individual cubes.

Triple Fused DominoThree Dominos reduced two two turns fused into one puzzle that allows to exchange pieces.

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