For a swivel-head design you will need a multi-axis CAM package which allows you to define a machine model describing the relationship of the machine components allowing calculation of clearance and moves within the CAM package.
Well conceived fixturing would allow the work you describe to be carried out with a conventional Fourth Axis (A) with the advantage that three 3-axis jobs with the correct Z zeros set can be concatenated in a text editor with the rotary indexing added manually, a remarkably simple process possible with the free CAD/CAM of your choice.

- Nick