The solver’s first step should be to investigate the most interesting
black moves in the diagram, namely the captures on d6, which leave both
bishop and knight pinned. That way the full theme will be revealed when
the solution is found.
Set play
1...Sxd6 2.e8S Kxe6 3.Sc7
1...Bxd6 2.e8B Kxe6 3.Bf7
The underpromotions in the set play are determined by which mating square will be unguarded after the king moves to e6. The key contains two threats which the defences at d6 prevent, 2.Qe5+ because of the removal of the guard on c7, and 2.e8Q because of stalemate. It removes knight guards from c6 and f7, which prevents the set continuations from working, but the new knight guard on e5, allowing queen mates at e5 and g8, prompts a reciprocal change of underpromotions. A very interesting change mechanism.