I was trying to find the answer for question:
How to evaluate intertype relationship by smallest number of dichotomies?

The model must meet the following conditions:
- Compare by number of the same dichotomies - the more, the better
(Why not "the less, the better"? Identical relationship.)
- Be generic
(Until you are no this type of person, who prefer conflictor over dual, this model will work for you)

Here's what I came up with:
Ignored Dichotomy:
Let assume that Dual and Identical must belong to the same category (two best relationships). To tell the difference (distinguish your dual from your identical) there must be dichotomy that will be ignored during comparison.
It must be complement - I choose Introverted/Extraverted, because it is first dischotomy in classic 4 letters type

F-T - Feeling-Thinking preference:
(Fi-Te vs Fe-Ti) Merry vs Serious

S-I - Sensing-Intuition preference:
(Si-Ne vs Se-Ni) Judicious vs Decisive

Importance - Which preferences are more important: F-T vs S-I
Let assume that polr is the most painful. If you have F or T polr your Importance is F-T. S or I polr -> Importance is S-I.
Then it can be simplified by Judging/Perceiving:
Judging: S-I importance (painful S or painful I)
Perceiving: F-T Importance (painful F or painful T)

Model:
[Ignored Dischotomy] [F-T preference] [S-I preference] [Importance]
[Introverted/Extraverted] [Merry/Serious] [Judicious/Decisive] [Judging/Perceiving]

Result:
3 matching dichotomies:
Dual, Identical
2 matching dischotomies:
F-T and S-I: Activity, Mirror (Your quadra)
(F-T or S-I) and Importance: Semi-dual, Kindred; Look-a-like, Illusionary
1 matching dischotomies:
F-T or S-I: Supervisee, Beneficiary; Supervisor, Benefactor
Importance: Extinguishment, Super-Ego
0 matching dischotomies:
Conflicting, Quasi-identical

Example:
I am IEI -> IMDP -> Introverted, Merry, Decisive, Perceiving
This model is flexible so let add + in prefered category, so there will be 8 tiers

3: NiFe, SeTi
2+: NeTi, SiFe (I have very strong preference for F-T) (Merry + Perceiving)
2: FeNi, TiSe (Merry)
2-: SeFi, NiTe (Perceiving)
1+: TiNe, FeSi (Merry)
1: NeFi, SiTe (Perceiving)
1-: TeNi, FiSe
0: FiNe, TeSi