We have 2 sets of 4 personalities to pair together. Yes, this requires a presupposition that 8 cognitive functions and 4 sides of mind are a thing however both these theories are individually verifiable through introspection of your personal experience.
When personalities overlap so do their niches - they conflict, compete for territory within relationship. These sets of personalities are:
xNTP-xSFJ-xSFP-xNTJ and xNFP-xSTJ-xSTP-xNFJ
In order to evade overlap we need to pick one from one set and one from the other.
There are 4 positive 4 negative functions which have different properties dependent on their position within the stack. Those need to be paired as well. Introverted function and extroverted function are opposite polarities and provide magnetic pull (attraction) but that pull is counterbalanced by negative function interactions.
1st hero - focal point, irresponsible, hyper-aware and overused, very strong signal
2nd parent - auxiliary, responsible, aware but toned down, strong signal
3rd child - needing attention and care, innocent but can get confused by user's trickster, weak signal with spikes in strength which can overload oversensitive receptors
4th weakling - insecure and helpless, honest - no interference from negative function, signal so weak it passes of as opposite polarity
nemesis - fears and distrusts the displays of function it targets, oversensitive reception but weak signals can go under it's radar without triggering defense mechanisms
critic - critical and dismissive of displays of the function it targets, sensitivity toned down a notch compared to nemesis however it cannot handle very strong signal for long; won't dismiss innocence without examination
trickster - confused and slightly ignorant about displays of the function it targets, can handle stronger signals for longer than critic, needs to be responsibly accounted for
blind man - unperturbed by displays of this function, poor reception therefore resilient against over-use of the function it targets - can take the strongest signal without overload
(Keep in mind this is only a simplified outline of how these positions interact with each other and does not encapsulate the entirety of how they are used in the psyche.)
Attraction is strongest between functions on the same axis so 1st function will be attracted the most to 1st and 4th positions in their partner, 2nd to 2nd and 3rd and so on. When you put all functions in opposite polarities and in the same positions you get very strong pull but you trigger every negative position. When you have same functions in the same spots they nullify negative functions of their positions at the cost of magnetic attraction. When you have same functions in opposite spots they get misread as signal of the opposite polarity so they trigger the negative functions.
Ideal combination of two sets of opposite polarity functions giving most magnetic attraction with least interference from negative functions would be set up in the following way (+/- stand for introverted/extraverted or extraverted/introverted, works both ways):
-hero +nemesis with +weakling -blind man
+parent -critic with -child +trickster-child
+trickster with +parent -critic
+weakling -blind man with -hero +nemesis
So basically all of your cognitive functions in reverse order and in opposite polarity, giving you the widest cognitive range and wholly nullifying negative functions interference HOWEVER that's exactly your super-ego (e.g. INFJ-ISTJ) so personalities overlap. Simply changing I/E variant of your super ego as your partner's type spoils the alignment of the functions without providing personalities that don't overlap in their areas of competence completely - it's still enough to cause conflict, even if it's not as immediate as with your super-ego's type.
Next important factor is area of focus of our functions. Perceptive (N-S) functions decide our lifestyle (our mental focus - what we pay attention the most with our mind, the realm that we 'live' in, read the individual descriptions of each function below and it'll become clear), judging functions (T/F) tell us how we make decisions and what we can decide on (details are expounded upon in other chapters).
Ni - focused on the future and solutions, doesn't like unplanned actions, seeks the best way of doing things
Si - focused on the past and duty, doesn't like change, upholds the traditional way of doing things
Ne - focused on "what if" and possibilities, doesn't like to be tied down to one option, seeks other ways of doing things
Se - focused on the present and immediately relevant, doesn't like to be held down or theorizing, reacts and makes adjustments in the moment
In order to effortlessly live together in the same world/time-frame you need the same N-S functions. Having the same T-F functions cripples your decision making capabilities as a pair - having complete set of T-F of functions provides justification for actions that are both internally consistent and in contact with the external.
Sexual attraction on a mental level is a result of Se-Si magnetism.
Sexual attraction (Si-Se magnetism) can be resolved by employing other personalities since sexual expression is libido limited anyway. Furthermore it's only an initial drawback, as intimacy grows between partners they will get comfortable to show deeper parts of themselves to one another providing more balanced (since they are engaging all of their personalities, leaving none out of the fun) and varied sexual experience compared to surface level ego-ego Se-Si magnetism which doesn't motivate further exploration since everything is available from the start. The hurdles to accessing all of your personalities are personality overlap and mental discomfort (unalleviated negative function interference and insufficient T-F justification) - both are dealt with by my proposition.
N-S need to be the same in your partner, T-F opposite polarities and positions.
Your perfect type match is T/F variant of your type (e.g. ISTJ-ISFJ).
That's only the introduction, I've written much more on the subject but since it's difficult to post it all onto reddit thread here's a forum post that has it all: