By Socionics
intertype relations chart the best match for ENFJ is the ISTP. These two types have exactly same cognitive functions but in reverse formation, making them form what's called a Duality relationship (described under
LSI-EIE, ISTP becomes ISTj in socionics since that is their Ti leading Se creative type). Unfortunately these two types, ENFJ and ISTP, rarely meet, so their unions are very few.
I think this whole "sharing the same functions" thing is misleading. Technically, there are only 4 functions (thinking, feeling, sensing, intuition), and 2 function attitudes (introverted or extroverted). The combination produces the 8 cognitive processes, or really, the 8 ego types. However, you do not share the same processes as your opposite type, not in the meaning most understand "share" to be. Instead, you prefer opposing processes, and while those opposing processes occur within yourself, you do not "use" them in a way that shapes your visible personality or perception of reality; you could actually say that you suppress them in favor of your ego (dominant process) instead. Defining someone that way is like defining something by what it isn't vs what it is. Sure, you can do that, but you can't say two people think similarly when they share opposite strengths/flaws. Instead of sharing anything, their preferences oppose each other.
For instance, Fe & Ti oppose, but Fe & Fi don't, as they are the same function with different attitudes. You could say there is overlap there, whereas Fe & Ti do not "overlap". The Fe type will experience Ti in their own mind as something distasteful or uncomfortable, and in another person, it will prove to be the opposite of how they prefer to experience/view life. At best, it often seems "exotic" (this is the draw to opposite/dual types, IMO).
So your dominant & auxiliary are what shape your visible personality, and the inferior is sort of an antagonist or an opposing force in your mind that you avoid, and when you must deal with it you "grow" or "shrink" as a person. This dynamic is within a person more so than between people. Someone who is opposite or your dual will often prove grating, then, or their initial appeal will occur because they are hard to understand & that is fascinating. Over time, such appeal does not tend to last because it opposes how you prefer to be. We're talking "oil & water" basically.
Because of this, a NF who prefers intuition & feeling will often jive better with another NF, despite their Feeling & iNtuition not having the same attitude (ie. an ENFP + INFJ). Statistics show this as well...the more LETTERS a person has in common with their mate, the more satisfaction is reported. Yes, letters are not cognitive processes, but the middle ones DO represent functions, which proves more significant in relationships anyway.
And contrary to what you write, according to stats out there,
the xNFJ female & xSTP male combo is one of the most common "opposite" (or "dual, depending on whether you prefer MBTI or socionics)
couplings. The other is xNFP female & xSTJ male, and according to the same statistics, both of these are
reported as unhappy most of the time.
The happiest couples reported? NF+NF, of any NF type.
IMO, this mistaken idea that someone is needed to balance you out (ie. your "opposite") has been carried over into the theory, where people think someone with the same function-attitudes but in reverse is complementary AND similar. But really, while opposites can attract initially, they often just prove antagonistic in a negative way, and the benefits of that dynamic is more fruitful mentally/emotionally when it occurs within yourself, not in a relationship with someone else. In a relationship with someone else, a similar & compatible outlook in life (leading to happiness ) is shown to be far more related to your first two functions (the middle letters), regardless of their attitude.
/tangent