  There is an increasing interest in nonlinear supersymmetries in cosmological
model building. Independently, elegant expressions for the all-tree amplitudes
in models with nonlinear symmetries, like D3 brane
Dirac-Born-Infeld-Volkov-Akulov theory, were recently discovered. Using the
generalized background field method we show how, in general, nonlinear
symmetries of the action, bosonic and fermionic, constrain amplitudes beyond
soft limits. The same identities control, for example, bosonic E_{7(7)} scalar
sector symmetries as well as the fermionic goldstino symmetries.
  We present a universal derivation of the vanishing amplitudes in the single
(bosonic or fermionic) soft limit. We explain why, universally, the double-soft
limit probes the coset space algebra. We also provide identities describing the
multiple-soft limit. We discuss loop corrections to N\geq 5 supergravity, to
the D3 brane, and the UV completion of constrained multiplets in string theory.
