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 Poincaré 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. 1 d.roest@rug.nl 2 d.stefanyszyn@rug.nl 3 p.j.werkman@rug.nl 1 Note that this simple connection between symmetries and enhanced soft limits does not apply to gauge theories, where gauge symmetries can be thought of as an infinite number of coordinate dependent symmetries, but is certainly applicable to scalar and spin-1/2 fermions. We will comment on gauge theories in section 5.1 compatible with a canonical propagator. This is important when understanding the soft behaviour of a dilaton, for example, where once we canonically normalise all terms in all transformation rules are field-dependent 2 , see e.g. [15]. It does therefore not fit into the above classification but it is known that the dilaton has σ = 0 soft behaviour [16][17][18].However, the soft amplitude bootstrap is not the only way of classifying these special EFTs without reference to Lagrangians. Any symmetries which are non-linearly realised on the fields must form a consistent Lie-algebra with the assumed linearly realised symmetries. One can therefore ask which Lie-algebras are consistent within the framework of the coset construction for non-linear realisations [19][20][21] augmented with the crucial inverse Higgs phenomenon 3 [22]. For scalar EFTs Lie-algebraic approaches have been presented in [23,24] while in [25] these methods were used to prove that a gauge vector cannot be a Goldstone mode of a spontaneously broken space-time symmetry without introducing new degrees of freedom. This implies that the Born-Infeld (BI) vector is not special from the perspective of non-linear symmetries and enhanced soft limits (the same result was found in [8] where it was shown that the BI vector has a vanishing soft weight).Recently, we presented an algorithm f...