You don't know how happy it makes me to find a kindred spirit.
Even those relations can be represented with dichotomies if rationality is taken into account (the dichotomies that describe a rational kindred pair is the same the describe an irrational business pair, ect). The only thing off the top of my head that cannot be represented as dichotomies is information flow.
In general, I think that dichotomies are complementary to a model. Even if intertype relationships can be understood with dichotomies, the information element projection in model A is much more useful.