This is a good thing!
There are billions of people, each with their own unique
experiences, and it is impossible to account for all of the ways in
which some of those people are plural. There are too many factors,
and the idea of a singular state of self is merely an assumption.
There are ways of becoming plural that are nonvoluntary and others
that are voluntary. Plurality can be spiritual, psychological,
neurological, natural, metaphysical, et al.
Source is only one facet of plurality, and it can be important or
trivial. That's up to the plurals in question.
Limiting our understanding to a single narrative of plurality is at
odds with respecting the ability of others to define their own
experiences.
Terms such as "plural," "system," and "multiple" belong to all
plurals who want to use them.
Hoarding plural terminology and claiming it's exclusive to a
specific category of plurality is unnecessary gatekeeping that
doesn't benefit anyone, including the people who do the gatekeeping.
It's dishonest and doesn't reflect reality or history.
Introject is a generic term for any system member who has a source
external to the system.
There are no rules for how an introject identifies with their source
material. Introjects can identify "as" their source or "like" their
source or anything else.
A fictive/factive/other introject may keep the same identity as
their source or they may not. Neither of these is superior to the
other.
Insisting that all introjects must feel a certain way about their
source is harmful and prevents their natural development as living
beings.