  We investigate the soft behaviour of scalar effective field theories (EFTs)
when there is a number of distinct derivative power counting parameters,
$\rho_1< \rho_2<\ldots < \rho_Q$. We clarify the notion of an enhanced soft
limit and use these to extend the scope of on-shell recursion techniques for
scalar EFTs. As an example, we perform a detailed study of theories with two
power counting parameters, $\rho_1=1$ and $\rho_2=2$, that include the shift
symmetric generalised galileons. We demonstrate that the minimally enhanced
soft limit uniquely picks out the Dirac-Born-Infeld (DBI) symmetry, including
DBI galileons. For the exceptional soft limit we uniquely pick out the special
galileon within the class of theories under investigation. We study the DBI
galileon amplitudes more closely, verifying the validity of the recursion
techniques in generating the six point amplitude, and explicitly demonstrating
the invariance of all amplitudes under DBI galileon duality.
