(trying to explain the different models in terms of each other)
my beginning assumption: the examples given on the lenore exegesis site are correct examples of correctly typed people (not always true, as I don't agree with some of thier type guesses)
But still, on some level, even though they are using different models, they are talking about the same thing.
The descriptions of the dominant and auxiliary functions already match fairly well with the Beebe model, so no discrepency there. With the big exception that: the Lenore people don't really realize the limitations of the auxiliary function. As "Building Blocks of Personality type" (Haas+Hunziker) states it, the auxiliary function can lead us to become "enablers to chronically dependent people" and I notice this a lot with older folks. For the kids (like me, I'm 19) the advice to turn to the auxiliary function is probably good advice. But even then, it's only good advice to a point. In general, the auxiliary function is, as edcoaching has pointed out, quite a *caricature* of that function. When people become to insistent upon not breaking the rules of this process, their advice to others becomes predictable and irrellevant, and for them the process begins limiting thier own growth.
Or, stated another way, everything less positive that I just said about the auxiliary function is really about the subconscious influence that the witch/senex archetype can have on the auxiliary function. After all, that's what the Beebe model is about: astutely identifying the specific function-archetypes that subconsciously influence our conscious tendencies. So is what I mentioned a paragraph ago about the less positive side of the auxiliary or about the with senex? It's definately about both.
Tertiary defense: on the Lenore site, they talk a bit about people falling prey to what they call a 'tertiary defense'. (I won't post all the examples from the site here, but feel free to read them yourself)
I don't think all of the examples of 'tertiary defense' are correct identifications of the tertiary function, or that they're all neccesarily bad behaviors (the Lenore site has the implicit yet NOT at all subtle point that the 'tertiary defense' is a bad thing to be doing no matter what the situation) but the IN_P one is one I've definately noticed with IN_Ps. so I'll mention it:
"Fi + Si: "I must proceed cautiously into the unknown, or I will just mess up and feel like crap!""
"Ti + Si (+ inferior Fe): "People's customs about political correctness are so arbitrary, I have no hope of understanding them: every guess about how I should behave is just a shot in the dark... It's best to just play it safe with people, because if I mess up, they will just think I'm a nerd with no social skills.""
Also, what I sometimes notice is IN_Ps preaching thinking outside the box but for themselves embracing things/people/ideas they are already familiar with (see Vicky Jo's INFJ or INFP? a closer look tertiary function page for more about that. She calls it "tradations with a little t")
What the Lenore people are not noticing: The unconscious (yet obvious) influence of the witch and trickster functions.
Witch/senex Ni: takes the form of, well, fear. While thier powerful auxiliary intuitive function is busy rejecting and looking down upon the introverted intuitive function, the introverted intuitive function is falling further into the unconscious, into a position where it starts controlling the weaker tertiary function, and the tertiary function doesn't know any better and accepts the negative and pessimistic introverted intuitions as facts of life.
Trickster Se: While they like to see themselves as easygoing, they just can't seem to loosten up and be cool in the physical world. In athletics, they might feel awkward. Or they might see flirtation as an annoying game: every piece of advice thier Se friend gives them sounds like a great idea, but all that advice that sounded simple and obvious never works when they try it. Thier percieved failure then leads them to become more pessimistic, and fuels the tertiary defense.
Where I come into conflict with the lenore people is the advice they give: They tell everyone to turn to the auxiliary. I say in the IN_P dynamic I just explained, the auxiliary has almost nothing to offer. I say, in that situation, they should find an IN_J and work on using introverted intuition until it becomes less negative for them. Also, they take a further look at thier inferior and opposing personality processes for more help. Again though, the most important step would be working thier introverted intuition until it became less negative, and coming up with some extraverted sensing solutions of thier own instead of giving that function up to thier friends and society in general.