  In the present investigation we consider the possibility of having new
massive, higher spin W-supergravity theories, which do not exist as
four-dimensional perturbative models. These theories are based on a double copy
construction of two supersymmetric field theories, where at least one factor is
given by a N=3 field theory, which is a non-perturbative S-fold of N=4 super
Yang-Mills theory. In this way, we can obtain as S-folds a new N=7
(corresponding to 28 supercharges) W-supergravity and its N=7 W-superstring
counterpart, which both do not exist as four-dimensional perturbative models
with an (effective) Langrangian description. The resulting field resp. string
theory does not contain any massless states, but instead a massive higher
spin-four supermultiplet of the N=7 supersymmetry algebra. Furthermore we also
construct a four-dimensional heterotic S-fold with N=3 supersymmetry. It again
does not exist as perturbative heterotic string model and can be considered as
the heterotic counterpart of the N=3 superconformal field theories, which were
previously constructed in the context of type I orientfold models.
