How did the parts integration model develop?
The parts integration model itself is a development of an earlier process called the Visual Squash. Its advantage is that it connects two opposing parts together, where the six step reframe left the part that was of concern to generate new behaviours while still separate. Parts Integration is discussed by Robert Dilts in the book Beliefs (Dilts, Hallbom and Smith, 1990, p 101-126, p 165) where Dilts gives a transcript of its successful use to treat an allergy to cats, tested in the training room immediately after.
Since the development of Parts Integration, other NLP processes to deal with parts issues have continued to evolve, including Core Transformation (Andreas 1992) and Time Line Therapy TM (James and Woodsmall, 1988). Generally, these utilise the outcome chain process, where the person is asked for the part's "outcome" and then asked "If you get that fully and completely, what do you get, through having that, that's even more important?".