  One of the simplest examples of non-invertible symmetries in higher
dimensions appears in 4d Maxwell theory, where its $SL(2,\mathbb{Z})$ duality
group can be combined with gauging subgroups of its electric and magnetic
1-form symmetries to yield such defects at many different values of the
coupling. Even though $\mathcal{N}=4$ Super-Yang-Mills (SYM) theory also has an
$SL(2,\mathbb{Z})$ duality group, it only seems to share two types of such
non-invertible defects with Maxwell theory (known as duality and triality
defects). Motivated by this apparent difference, we begin our investigation of
the fate of these symmetries by studying the case of 4d $\mathcal{N}=4$ $U(1)$
gauge theory which contains Maxwell theory in its content. Surprisingly, we
find that the non-invertible defects of Maxwell theory give rise, when combined
with the standard $U(1)$ symmetry acting on the free fermions, to defects which
act on local operators as elements of the $U(1)$ outer-automorphism of the
$\mathcal{N}=4$ superconformal algebra, an operation that was referred to in
the past as the "bonus symmetry". Turning to the nonabelian case of
$\mathcal{N}=4$ SYM, the bonus symmetry is not an exact symmetry of the theory
but is known to emerge at the supergravity limit. Based on this observation we
study this limit and show that if it is taken in a certain way, non-invertible
defects that realize different elements of the bonus symmetry emerge as
approximate symmetries, in analogy to the abelian case.
