  We unwind the induction implicit in the "one-step" asymptotic expansions of
arXiv:1701.02417 to describe how to turn asymptotic expansions, such as (but
not limited to) the Harish-Chandra--Howe local character expansion, for
depth-(0) supercuspidal characters into Kim--Murnaghan-type asymptotic
expansions for arbitrary positive-depth, tame, supercuspidal characters. Doing
so requires analogous results for Fourier transforms of orbital integrals on
the Lie algebra of a reductive group, which are of independent interest.
