While it would be possible to add a milling operation, a live tooling lathe could do the turning and milling in one set-up, greatly improving the accuracy.
A live tooling lathe is a CNC lathe with an added “sub spindle”, meaning; it spins the part to turn the profile, and can also call out a tool that spins on its own (like a milling machine spindle inside the lathe.) this allows you to utilize off center milling, using the lathe rotary axis as a indexer, and pocketing capability you wouldnt otherwise be able to accomplish in a traditional lathe. All of this is programmable in, and its very impressive equipment.
I’ll attach an image to show an example.