Incomplete, as should be obvious from the missing types in Gamma quadra.
This is a tentative list.
I hypothesize that LIIs -- and all of the other types, for that matter -- switch from amongst any of the sixteen energy processing orders as the need arises, especially when discoursing in monologue. This allows them to see the situation and its meaning from as many angles as possible, and to demonstrate their understanding of it. Frequently the thesis of their argument will center around observations made in the context of the dominant EM type (dominant meaning the strongest possible function ordering), with various supporting theories proposed by other LIIs (and ILEs, as needed) backing it up. The weaker functions are usually avoided altogether, and the id functions are used exclusively as a means of answering criticism, or to explain the origin of the thesis. (its empirical TeNi basis)