  We use on-shell amplitude methods to systematically analyze the possibility
of extended supersymmetry for 4d Galileon models, expanding on previous
$\mathcal{N}=1$ results. Assuming spins $\le 1$, we prove that there exists no
$\mathcal{N}=4$ supersymmetric extension of any 4d Galileons. Thus the
Galileons cannot be part of the effective action of a single flat maximally
supersymmetric D3-brane, and that explains why such terms do not appear in the
$\alpha'$-expansion of the abelian open superstring amplitude. For
$\mathcal{N}=2$ Galileons, we show that the complex scalar $Z = \phi + i \chi$
of the vector supermultiplet cannot have $\phi$ and $\chi$ both enjoy enhanced
shift symmetry; instead, $\chi$ can at best be an $R$-axion with constant shift
symmetry. Using the soft bootstrap, we demonstrate that the quartic
DBI-Galileon is incompatible with $\mathcal{N}=2$ supersymmetry. A similar
analysis performed at 7-point shows that a 2-parameter family of
$\mathcal{N}=2$ supersymmetric quintic Galileons coupled with DBI passes the
soft bootstrap. Finally, we show how supersymmetric coup\-lings between
Galileons and gravitons arise in generalizations of our constructions, and we
conclude with a discussion of Galileons and DBI-Galileons in the context of
UV-completability vs.~the Swampland.
