Barit1, you are correct, some very critical components are bought from speciality suppliers, forgings, from which discs, casings and engine mounts are machined from, investment castings from which structural components and turbine airfoils are produced and no doubt a few other more critical components from other processes. At one time, all three engine manufacturers had investment casting foundries, but I think only Rolls Royce has a production facility today.
There has been some purchases of independent suppliers by the engine manufacturers where the technology knowhow meshes well with the technology thrust of the engine company, such as composites for example.