A supervisor relationship is supposed to be difficult, but generally I seem very compatible with people I think are ENFjs.
First of all, I think it is important to focus on your relations with people whose type you are 100 % certain of. If you are not sure, "dismiss" them for the moment.

I've been very close with some INFps. In some ways, I seem very similar to them, suggesting that they're almost the same type (-based); but I could also see a relation of 'benefit' operating too.
Well, that's almost exactly my own experience. I can't be 100 % sure of which it is, but I think the former option is more likely.

I get along very well with ESFps, as coworkers, friends, etc. (suggesting possibility of a dual relationship), and tend to admire their friendliness and merriness.
I haven't had any longtime, close friendship with an ESFp, but I have noticed that there is a group of people, which I am now almost certain consist of ESFps, who I have many times during the years felt some strange attraction to. I have felt "at ease" with them in a special way that is different from the way I can feel at ease with some other types.

One other type that I get along well with in most situations is the ENFp. I know more ENFps than ESFps, and I know them better. I tend to recognize them very fast, often using only V.I. At least the female ENFps come in two forms. One is the "Cher" type, the other is more "rounded". Both these forms of ENFp are described in Socionics, for example on SG's site. We usually have stimulating conversations and discussions. We can get irritated at each other, but that don't last long. It is difficult for me to put the character of that relation into exact words, but from several real life experiences I know when it is there. One thing, though, they are clearly recognizable (after a while) as N people. So, if you can spot that you won't confuse them with ESFps or some other S type.

Around ESFjs, I tend to appreciate that they graciously do things that I don't like to do, and I generally enjoy emotional expression in others (suggesting dual), but somehow I very rarely have contact with ESFjs or ISFps.
The ESFj is a type that I recognize without problem (at least in women), and I have known several for years. One of them is my own mother. As I have said in some other posts before, I can't relax and feel at ease with them. I clearly feel that we live in different "life rhythms", and we have difficulties in conversations. Either we don't find anything to talk about, or if we do, we often find that we disagree and they don't want to discuss the issue further. If there is anything to this talk about two different life rhythms (J and P attitudes towards life), which I strongly believe there is, that alone should probably be enough to settle whether you and I are INTps or INTjs.

I'm often curious about ISFPs, and when I do talk with them, I usually enjoy the conversation and find it interesting (suggesting activity), but our worlds rarely intersect (suggesting super ego).
I have known a couple of ISFps for years, too. I find it rather easy to recognize them by V.I., and they also have characteristic shifting facial expressions. I'm not sure our type of relation fits the descriptions of Super-ego or not, but I think it is possible. We don't spend that much time together though, so it's hard to tell.

Another type that I know well is the ISFj. I have never experienced any difficulties in the initial contact, and the character of our relation fits Activity rather well. Some of my male friends are ISFjs, and my partner for many years is also an ISFj. She and I can tire of each other in the way described, and we also experience some of the problems in everyday matters that are described in Activity relations. I think that I can tell for sure that she has the J attitude and I have the P attitude. But in that area we both compromise somewhat.

One of the problems is that clear definitions of and consensus on what the intertype relationships are supposed to be like are even harder to find than definitions for the types or functions.
I have found three different short descriptions on the internet. We have those on SG's site, we have Rick's, and there is at least one more (forgot where). Put them together and compare them is my advice at the moment.

By the way, why don't you believe in mixtures? Naturally, the types exist as real structures that affect how people think and how thoughts are structured...but why does one have to have a single type at all?
Because of the intertype relations, and because the functions are like "vectors". We probably can't be mixtures of INTp and INTj, because their thought processes go in clearly different directions, resulting in the frustrating phenomenon that neither the INTp nor the INTj can understand how the other type really thinks. Another reason is V.I., where there seem to be rather clear boundaries between the types. Whether that is true or not can probably be decided in the future with the help of "V.I computers", when we also probably will have a more exact knowledge of the human DNA.