Moirallegiance intrigues me on a high level, as does auspisticism. I'd like to know more about how one differentiates their pale feelings from red ones, since it has been said that pale feelings can be easily confused for red ones early on, and vice versa (I think a prime example of this is Eridan, who was Feferi's moirail but ended up having red feelings for her in the end, however their moirallegiance was ended and the red feelings were not reciprocated). I'd also like to know how the canon moirails came about.
As for auspisticism, it's the quadrant we know the least about. The only thing we really know is that it's a mediator between a pair of kismeses. We however do not know how a kismesis ends up needing to become an auspisticism (we can assume it's highly violent actions, however violence is not looked down upon in troll society), nor more complicated duties of the auspistice (we know that they have to keep the blackrom in check, however we aren't sure how they do this). In fact, other than that the only thing we really know about auspisticism is that Kanaya is really good at it.
All in all, it's the conciliatory relations that spark my interest. The concupiscent relations of matespritship and kismesisstude both are simpler to understand, since we know matespritship is like human love and kismesisstude is deep hatred with romantic feelings. We can pretty much imagine the possibilities with those since the concepts are somewhat more familiar (although the concept of kismesisstude does confuse some, if you don't over-think it it's actually rather simple). However, we humans don't have much like moirails and auspistices. When one thinks of moirallegiance, they might imagine a set of best friends. However it is much more than that. Moirails are the closest thing trolls have to siblings, and it's basically a sibling like platonic love in which they look after each other. However with our human sibling relations, moirallegiance isn't really something considered in the mix. Since we have actual siblings, we don't see the importance of having someone like a moirail. However with trolls, they grow up alone with only their lusus. Keep in mind that troll society is rather violent, so going out could be a death sentence. The closest thing we have to auspisticism is mediation between arguing parties, which doesn't quite cover the true essence of auspisticism. So, overall, I would love to learn more about the conciliatory relationships of the pale and ashen quadrants.