I was reading some of labcoat's work on Tac/Nar over in this thread:
If I understand correctly, it basically inverts the socion, so that Alpha shares rational elements with Delta and irrational ones with Beta, and so on. It means ILIs and SLIs are sort of semi-duals, and that ILIs and SLEs sort of have illusionary relations.
Assuming that Stat/Dyn and Tac/Nar are of roughly equal significance, (correct me if I'm wrong), the socion becomes extremely symmetrical in a weird, multilayered way. It implies that an LII should react to an EIE and an EII in very similar ways. The first case is TiNe+FeNi, while the second is TtNt+FnNn. Same general setup, with Tx and Fy in the base and Nx and Ny in the creative. Note what this does to Supervision and Benefit. Supervisees should benefit supervisors, and beneficiaries should supervise benefactors.
The quadras on either side of a type will have basically the same set of relations, each of which will be a mish-mash of two classical relations.