We really have only three possible placements of the layers of spheres, because the centers of spheres in any layer project into only one of three distinct sets of points on the "ground". We label those three sets A, B, C and that's it. No more.
What we _can_ have is orderings among A, B, C other than the simplest ones you quote. For example, there could be ABACABAC where you have all three sets of locations but not equally represented (e.g. more A's than B's), an arrangement called double hexagonal close-packed. This presentation explains the double hexagonal close-packed arrangement and identifies lanthanum as a prototypical example. Wikipedia also lists this structure for lanthanum. The structure of samarium, discussed here, involves a more complex packing (ABCBCACAB).