An order 3 dipyramid can be split into two regular tetrahedra.
An order $n$ dipyramid can be split into $n$ isosceles tetrahedra.
A rhombic dodecahedron can be split into four rhombic hexahedra.
A 4-scalenohedron with edges of length $(\sqrt5, \sqrt8,\sqrt9)$ can be split into 4 congruent isosceles tetrahedron.
A triakis tetrahedron with opposite corners $-(2,2,2)$ and $(3,3,3)$ can be cut into 4 isohedral triangular dipyramids.
A 4-scalenohedron with edges of length $(1, 1,\sqrt{12/7})$ can be split into 5 congruent isosceles tetrahedron.
An isosceles tetrahedron with edges of length $(4, 2\sqrt3,2\sqrt3)$ can be split into 8 congruent copies of itself. 4 copies of this same tetrahedron makes an order 4 dipyramid, and it's also a space-filler.
A cube or trapezohedron can be split into 8 or more smaller cubes or trapezohedra.
These are all cases where an isohedron is split into isohedra. Are there any other examples?