  A holographic duality was recently established between an ${\cal N} =4$
non-geometric AdS$_4$ solution of type IIB supergravity in the so-called S-fold
class, and a three-dimensional conformal field theory (CFT) defined as a limit
of ${\cal N} =4$ super-Yang-Mills at an interface. Using gauged supergravity,
the ${\cal N} =2$ conformal manifold (CM) of this CFT has been assessed to be
two-dimensional. Here, we holographically characterise the large-$N$ operator
spectrum of the marginally-deformed CFT. We do this by, firstly, providing the
algebraic structure of the complete Kaluza-Klein (KK) spectrum on the
associated two-parameter family of AdS$_4$ solutions. And, secondly, by
computing the ${\cal N} =2$ supermultiplet dimensions at the first few KK
levels on a lattice in the CM, using new exceptional field theory techniques.
Our KK analysis also allows us to establish that, at least at large $N$, this
${\cal N} =2$ CM is topologically a non-compact cylindrical Riemann surface
bounded on only one side.
