I have a development for this. It seems the inter-types work for the equivalences presented here. For instance; 6w7 would be Supervisor to 3w4, and 9w1 supervisor to 8w9.
It also seems that subwings determine the socionics equivalence. For example; 8w9sw9w1 would be SLE-Se, but 8w9sw7w8 would be something else (SLE-Ti?). In the future if I figure out the patterns I might do a complete list with subwings.