  We present a novel approach to classify supersymmetric effective field
theories (EFTs) whose scattering amplitudes exhibit enhanced soft limits. These
enhancements arise due to non-linearly realised symmetries on the Goldstone
modes of such EFTs and we classify the algebras that these symmetries can form.
Our main focus is on so-called exceptional algebras which lead to
field-dependent transformation rules and EFTs with the maximum possible soft
enhancement at a given derivative power counting. We adapt existing techniques
for Poincar\'{e} invariant theories to the supersymmetric case, and introduce
superspace inverse Higgs constraints as a method of reducing the number of
Goldstone modes while maintaining all symmetries.
  Restricting to the case of a single Goldstone supermultiplet in four
dimensions, we classify the exceptional algebras and EFTs for a chiral, Maxwell
or real linear supermultiplet. Moreover, we show how our algebraic approach
allows one to read off the soft weights of the different component fields from
superspace inverse Higgs trees, which are the algebraic cousin of the on-shell
soft data one provides to soft bootstrap EFTs using on-shell recursion. Our
Lie-superalgebraic approach extends the results of on-shell methods and
provides a complementary perspective on non-linear realisations.
